Richard Timothy Durrett | Scholars@Duke

Richard Timothy Durrett
James B. Duke Professor of Mathematics

Current Research Interests

My favorite research topics are problems in probability that arise from questions in ecology, genetics, and cancer modeling. I also investigate processes taking place on complex networks (aka random graphs).

Current Appointments & Affiliations

James B. Duke Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2010
Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2010

Contact Information

105 Physics Building, Box 90320, Durham, NC 27708-0320
Dept of Math, Box 90320, Durham, NC 27708-0320
rtd@math.duke.edu (919) 660-6970
www.math.duke.edu/~rtd/

Background
Education, Training, & Certifications
- Ph.D., Stanford University 1976
Duke Appointment History
- Director of Graduate Studies in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2014 - 2018
Recognition
In the News
- MAR 16, 2016
  
  New Collaborative Seed Grant Program Gives Eight Awards
- NOV 4, 2015 Scientific Computing
  
  Mathematical models key to designing better cancer treatment strategies
- NOV 2, 2015
  
  Predicting Cancer’s Growth When Clues Are Hard To Come By
- MAR 26, 2015 Bioscience Technology
  
  Why some HPV infections go away and others become cancer
- SEP 25, 2014
  
  An Intersection of Math and Medicine: Modeling Cancerous Tumor Kinetics
- SEP 23, 2014
  
  Could Suburban Sprawl Be Good For Integration?
- FEB 20, 2013
  
  Factoring in the Deadly Math of Cancer
Awards & Honors
Expertise
Subject Headings
Research
Selected Grants
- Voters, games, and epidemics on random graphs awarded by National Science Foundation 2018 - 2021
- Mathematical Analysis of Spatial Cancer Models awarded by National Science Foundation 2016 - 2020
- Collaborative Research: The role of spatial interactions in determining the distribution of savanna and forest awarded by National Science Foundation 2016 - 2019
- The Mathematics of Breast Cancer Overtreatment: Improving Treatment Choice through Effective Communication of Personalized Cancer Risk awarded by National Institutes of Health 2016 - 2018
- Interacting Particle Systems on Lattices and on Graphs awarded by National Science Foundation 2015 - 2018
- Biodiversity and Evolution - Support for US Participants awarded by National Science Foundation 2013 - 2015
- Stochastic Spatial Models: on Complex Networks, Coevolution, and Modeling Cancer awarded by National Science Foundation 2013 - 2015
- Mathematical Models of Cancer Initiation, Progression, and Resistance to Therapy awarded by National Institutes of Health 2010 - 2015
- Ecology awarded by National Science Foundation 2010 - 2013
- Participant Support for Workshop for Women in Probability 2012 awarded by National Science Foundation 2012 - 2013
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Cristali, I., M. Junge, and R. Durrett. “Poisson percolation on the oriented square lattice.” Stochastic Processes and Their Applications, January 1, 2019. https://doi.org/10.1016/j.spa.2019.01.005.
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  - Wang, Zhuoqun, and Rick Durrett. “Extrapolating weak selection in evolutionary games..” Journal of Mathematical Biology 78, no. 1–2 (January 2019): 135–54. https://doi.org/10.1007/s00285-018-1270-6.
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  - Ma, R., and R. Durrett. “A simple evolutionary game arising from the study of the role of igf-II in pancreatic cancer.” Annals of Applied Probability 28, no. 5 (October 1, 2018): 2896–2921. https://doi.org/10.1214/17-AAP1378.
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  - Huo, R., and R. Durrett. “Latent voter model on locally tree-like random graphs.” Stochastic Processes and Their Applications 128, no. 5 (May 1, 2018): 1590–1614. https://doi.org/10.1016/j.spa.2017.08.004.
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  - Talkington, Anne, Claudia Dantoin, and Rick Durrett. “Ordinary Differential Equation Models for Adoptive Immunotherapy..” Bulletin of Mathematical Biology 80, no. 5 (May 2018): 1059–83. https://doi.org/10.1007/s11538-017-0263-8.
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  - Basak, A., R. Durrett, and E. Foxall. “Diffusion limit for the partner model at the critical value.” Electronic Journal of Probability 23 (January 1, 2018). https://doi.org/10.1214/18-EJP229.
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  - Beckman, E., E. Dinan, R. Durrett, R. Huo, and M. Junge. “Asymptotic behavior of the brownian frog model.” Electronic Journal of Probability 23 (January 1, 2018). https://doi.org/10.1214/18-EJP215.
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  - Cristali, I., V. Ranjan, J. Steinberg, E. Beckman, R. Durrett, M. Junge, and J. Nolen. “Block size in geometric(P)-biased permutations.” Electronic Communications in Probability 23 (January 1, 2018). https://doi.org/10.1214/18-ECP182.
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  - Lopatkin, Allison J., Hannah R. Meredith, Jaydeep K. Srimani, Connor Pfeiffer, Rick Durrett, and Lingchong You. “Persistence and reversal of plasmid-mediated antibiotic resistance..” Nature Communications 8, no. 1 (November 22, 2017). https://doi.org/10.1038/s41467-017-01532-1.
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  - Gleeson, James P., and Rick Durrett. “Temporal profiles of avalanches on networks..” Nature Communications 8, no. 1 (October 31, 2017). https://doi.org/10.1038/s41467-017-01212-0.
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  - Tomasetti, C., R. Durrett, M. Kimmel, A. Lambert, G. Parmigiani, A. Zauber, and B. Vogelstein. “Role of stem-cell divisions in cancer risk.” Nature 548, no. 7666 (August 9, 2017): E13–14. https://doi.org/10.1038/nature23302.
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  - Nanda, M., and R. Durrett. “Spatial evolutionary games with weak selection.” Proceedings of the National Academy of Sciences of the United States of America 114, no. 23 (June 6, 2017): 6046–51. https://doi.org/10.1073/pnas.1620852114.
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  - Bessonov, M., and R. Durrett. “Phase transitions for a planar quadratic contact process.” Advances in Applied Mathematics 87 (June 1, 2017): 82–107. https://doi.org/10.1016/j.aam.2017.01.002.
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  - Durrett, R., and W. T. L. Fan. “Genealogies in expanding populations.” Annals of Applied Probability 26, no. 6 (December 1, 2016): 3456–90. https://doi.org/10.1214/16-AAP1181.
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  - Ryser, Marc D., Mathias Worni, Elizabeth L. Turner, Jeffrey R. Marks, Rick Durrett, and E Shelley Hwang. “Outcomes of Active Surveillance for Ductal Carcinoma in Situ: A Computational Risk Analysis..” J Natl Cancer Inst 108, no. 5 (May 2016). https://doi.org/10.1093/jnci/djv372.
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  - Durrett, R., J. Foo, and K. Leder. “Spatial Moran models, II: cancer initiation in spatially structured tissue..” Journal of Mathematical Biology 72, no. 5 (April 2016): 1369–1400. https://doi.org/10.1007/s00285-015-0912-1.
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  - Cox, J. T., and R. Durrett. “Evolutionary games on the torus with weak selection.” Stochastic Processes and Their Applications 126, no. 8 (December 7, 2015): 2388–2409. https://doi.org/10.1016/j.spa.2016.02.004.
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  - Talkington, Anne, and Rick Durrett. “Estimating Tumor Growth Rates In Vivo..” Bulletin of Mathematical Biology 77, no. 10 (October 2015): 1934–54. https://doi.org/10.1007/s11538-015-0110-8.
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  - Ryser, Marc D., Evan R. Myers, and Rick Durrett. “HPV clearance and the neglected role of stochasticity..” Plos Comput Biol 11, no. 3 (March 2015). https://doi.org/10.1371/journal.pcbi.1004113.
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  - Durrett, R., and S. Moseley. “Spatial moran models I. Stochastic tunneling in the neutral case.” Annals of Applied Probability 25, no. 1 (January 1, 2015): 104–15. https://doi.org/10.1214/13-AAP989.
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  - Durrett, R., and Y. Zhang. “Coexistence of grass, saplings and trees in the Staver-Levin forest model.” Annals of Applied Probability 25, no. 6 (January 1, 2015): 3434–64. https://doi.org/10.1214/14-AAP1079.
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  - Magura, S. R., V. H. Pong, R. Durrett, and D. Sivakoff. “Two evolving social network models.” Alea 12, no. 2 (January 1, 2015): 699–715.
  - Varghese, C., and R. Durrett. “Spatial networks evolving to reduce length.” Journal of Complex Networks 3, no. 3 (January 1, 2015): 411–30. https://doi.org/10.1093/comnet/cnu044.
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  - Durrett, R. “Spatial evolutionary games with small selection coefficients.” Electronic Journal of Probability 19 (December 28, 2014). https://doi.org/10.1214/EJP.v19-3621.
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  - Durrett, Richard, and Yuan Zhang. “Exact solution for a metapopulation version of Schelling's model..” Proceedings of the National Academy of Sciences of the United States of America 111, no. 39 (September 15, 2014): 14036–41. https://doi.org/10.1073/pnas.1414915111.
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  - Aristotelous, Andreas C., and Richard Durrett. “Chemical evolutionary games..” Theoretical Population Biology 93 (May 2014): 1–13. https://doi.org/10.1016/j.tpb.2014.02.001.
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  - Durrett, R., T. Liggett, and Y. Zhang. “The contact process with fast voting.” Electronic Journal of Probability 19 (March 3, 2014). https://doi.org/10.1214/EJP.v19-3021.
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  - Aristotelous, A. C., and R. Durrett. “Fingering in stochastic growth models.” Experimental Mathematics 23, no. 4 (January 1, 2014): 465–74. https://doi.org/10.1080/10586458.2014.947053.
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  - Shi, Feng, Peter J. Mucha, and Richard Durrett. “Multiopinion coevolving voter model with infinitely many phase transitions..” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 88, no. 6 (December 30, 2013). https://doi.org/10.1103/PhysRevE.88.062818.
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  - Varghese, C., and R. Durrett. “Phase transitions in the quadratic contact process on complex networks.” Physical Review E Statistical, Nonlinear, and Soft Matter Physics 87, no. 6 (June 27, 2013). https://doi.org/10.1103/PhysRevE.87.062819.
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  - Mode, C. J., R. Durrett, F. Klebaner, and P. Olofsson. “Applications of stochastic processes in biology and medicine.” International Journal of Stochastic Analysis 2013 (April 29, 2013). https://doi.org/10.1155/2013/790625.
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  - Durrett, R. “Cancer modeling: A personal perspective.” Notices of the American Mathematical Society 60, no. 3 (March 1, 2013): 304–9. https://doi.org/10.1090/noti953.
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  - Durrett, R. “Population genetics of neutral mutations in exponentially growing cancer cell populations.” Annals of Applied Probability 23, no. 1 (February 1, 2013): 230–50. https://doi.org/10.1214/11-AAP824.
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  - Chatterjee, S., and R. Durrett. “A first order phase transition in the threshold θ ≥ 2 contact process on random r -regular graphs and r -trees.” Stochastic Processes and Their Applications 123, no. 2 (January 1, 2013): 561–78. https://doi.org/10.1016/j.spa.2012.10.001.
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  - Cox, J. T., R. Durrett, and E. A. Perkins. “Voter model perturbations and reaction diffusion equations.” Asterisque, no. 349 (January 1, 2013): 1–127.
  - Danesh, Kaveh, Rick Durrett, Laura J. Havrilesky, and Evan Myers. “A branching process model of ovarian cancer..” J Theor Biol 314 (December 7, 2012): 10–15. https://doi.org/10.1016/j.jtbi.2012.08.025.
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  - Durrett, Richard, James P. Gleeson, Alun L. Lloyd, Peter J. Mucha, Feng Shi, David Sivakoff, Joshua E. S. Socolar, and Chris Varghese. “Graph fission in an evolving voter model..” Proceedings of the National Academy of Sciences of the United States of America 109, no. 10 (March 2012): 3682–87. https://doi.org/10.1073/pnas.1200709109.
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  - Durrett, Rick, and Daniel Remenik. “Evolution of dispersal distance..” Journal of Mathematical Biology 64, no. 4 (March 2012): 657–66. https://doi.org/10.1007/s00285-011-0444-2.
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  - Chatterjee, S., and R. Durrett. “Asymptotic behavior of Aldous' gossip process.” Annals of Applied Probability 21, no. 6 (December 1, 2011): 2447–82. https://doi.org/10.1214/10-AAP750.
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  - Chatterjee, S., and R. Durrett. “Persistence of activity in threshold contact processes, an "Annealed approximation" of random Boolean networks.” Random Structures and Algorithms 39, no. 2 (September 1, 2011): 228–46. https://doi.org/10.1002/rsa.20357.
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  - Durrett, Rick, Jasmine Foo, Kevin Leder, John Mayberry, and Franziska Michor. “Intratumor heterogeneity in evolutionary models of tumor progression..” Genetics 188, no. 2 (June 2011): 461–77. https://doi.org/10.1534/genetics.110.125724.
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  - Durrett, R., and J. Mayberry. “Traveling waves of selective sweeps.” Annals of Applied Probability 21, no. 2 (April 1, 2011): 699–744. https://doi.org/10.1214/10-AAP721.
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  - Durrett, R., and D. Remenik. “Brunet-derrida particle systems, free boundary problems and wiener-hopf equations.” Annals of Probability 39, no. 6 (January 1, 2011): 2043–78. https://doi.org/10.1214/10-AOP601.
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  - Durrett, R., and Shirshendu Chatterjee. “Persistence of activity in random Boolean networks.” Random Structures and Algorithms 39 (2011): 228–46.
  - Durrett, Rick, Jasmine Foo, Kevin Leder, John Mayberry, and Franziska Michor. “Evolutionary dynamics of tumor progression with random fitness values..” Theoretical Population Biology 78, no. 1 (August 2010): 54–66. https://doi.org/10.1016/j.tpb.2010.05.001.
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  - Durrett, R., and J. Mayberry. “Evolution in predator-prey systems.” Stochastic Processes and Their Applications 120, no. 7 (July 1, 2010): 1364–92. https://doi.org/10.1016/j.spa.2010.03.011.
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  - Durrett, Rick. “Some features of the spread of epidemics and information on a random graph..” Proceedings of the National Academy of Sciences of the United States of America 107, no. 10 (March 2010): 4491–98. https://doi.org/10.1073/pnas.0914402107.
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  - Durrett, Richard, and Stephen Moseley. “Evolution of resistance and progression to disease during clonal expansion of cancer..” Theoretical Population Biology 77, no. 1 (February 2010): 42–48. https://doi.org/10.1016/j.tpb.2009.10.008.
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  - Chatterjee, S., and R. Durrett. “Contact processes on random graphs with power law degree distributions have critical value 0.” Annals of Probability 37, no. 6 (November 1, 2009): 2332–56. https://doi.org/10.1214/09-AOP471.
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  - Chan, B., R. Durrett, and N. Lanchier. “Coexistence for a multitype contact process with seasons.” Annals of Applied Probability 19, no. 5 (October 1, 2009): 1921–43. https://doi.org/10.1214/09-AAP599.
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  - Durrett, R., and D. Remenik. “Chaos in a spatial epidemic model.” Annals of Applied Probability 19, no. 4 (August 1, 2009): 1656–85. https://doi.org/10.1214/08-AAP581.
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  - Wu, Feinan, Nancy T. Eannetta, Yimin Xu, Richard Durrett, Michael Mazourek, Molly M. Jahn, and Steven D. Tanksley. “A COSII genetic map of the pepper genome provides a detailed picture of synteny with tomato and new insights into recent chromosome evolution in the genus Capsicum..” Tag. Theoretical and Applied Genetics. Theoretische Und Angewandte Genetik 118, no. 7 (May 2009): 1279–93. https://doi.org/10.1007/s00122-009-0980-y.
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  - Durrett, R. “SPecial invited paper coexistence in stochastic spatial models.” Annals of Applied Probability 19, no. 2 (April 1, 2009): 477–96. https://doi.org/10.1214/08-AAP590.
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  - Durrett, R., D. Schmidt, and J. Schweinsberg. “A waiting time problem arising from the study of multi-stage carcinogenesis.” Annals of Applied Probability 19, no. 2 (April 1, 2009): 676–718. https://doi.org/10.1214/08-AAP559.
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  - Durrett, R., and D. Schmidt. “Reply to Michael Behe.” Genetics 181, no. 2 (February 1, 2009): 821–22. https://doi.org/10.1534/genetics.109.100800.
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  - Durrett, R., and L. Popovic. “Degenerate diffusions arising from gene duplication models.” Annals of Applied Probability 19, no. 1 (February 1, 2009): 15–48. https://doi.org/10.1214/08-AAP530.
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  - Chan, Ben, R. Durrett, and Nicolas Lanchier. “Coexistence in a particle system with seasons.” Ann. Appl. Probab. 19 (2009): 1921–43.
  - Durrett, Rick, and Deena Schmidt. “Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution..” Genetics 180, no. 3 (November 2008): 1501–9. https://doi.org/10.1534/genetics.107.082610.
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  - Durrett, R., and N. Lanchier. “Coexistence in host-pathogen systems.” Stochastic Processes and Their Applications 118, no. 6 (June 1, 2008): 1004–21. https://doi.org/10.1016/j.spa.2007.07.008.
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  - Durrett, R., and M. Restrepo. “One-dimensional stepping stone models, sardine genetics and Brownian local time.” Annals of Applied Probability 18, no. 1 (February 1, 2008): 334–58. https://doi.org/10.1214/07-AAP451.
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  - Berestycki, N., and R. Durrett. “Limiting behavior for the distance of a random walk.” Electronic Journal of Probability 13 (January 1, 2008): 374–95. https://doi.org/10.1214/EJP.v13-490.
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  - Huerta-Sanchez, Emilia, Rick Durrett, and Carlos D. Bustamante. “Population genetics of polymorphism and divergence under fluctuating selection..” Genetics 178, no. 1 (January 2008): 325–37. https://doi.org/10.1534/genetics.107.073361.
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  - Durrett, R., and I. Zähle. “On the width of hybrid zones.” Stochastic Processes and Their Applications 117, no. 12 (December 1, 2007): 1751–63. https://doi.org/10.1016/j.spa.2006.05.017.
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  - Durrett, R., and P. Jung. “Two phase transitions for the contact process on small worlds.” Stochastic Processes and Their Applications 117, no. 12 (December 1, 2007): 1910–27. https://doi.org/10.1016/j.spa.2007.03.003.
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  - Sainudiin, Raazesh, Andrew G. Clark, and Richard T. Durrett. “Simple models of genomic variation in human SNP density..” Bmc Genomics 8 (June 6, 2007). https://doi.org/10.1186/1471-2164-8-146.
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  - De, Arkendra, and Richard Durrett. “Stepping-stone spatial structure causes slow decay of linkage disequilibrium and shifts the site frequency spectrum..” Genetics 176, no. 2 (June 2007): 969–81. https://doi.org/10.1534/genetics.107.071464.
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  - York, Thomas L., Rick Durrett, and Rasmus Nielsen. “Dependence of paracentric inversion rate on tract length..” Bmc Bioinformatics 8 (April 3, 2007). https://doi.org/10.1186/1471-2105-8-115.
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  - Huerta-Sanchez, Emilia, and Rick Durrett. “Wagner's canalization model..” Theoretical Population Biology 71, no. 2 (March 2007): 121–30. https://doi.org/10.1016/j.tpb.2006.10.006.
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  - Durrett, R., and D. Schmidt. “Waiting for regulatory sequences to appear.” Annals of Applied Probability 17, no. 1 (February 1, 2007): 1–32. https://doi.org/10.1214/105051606000000619.
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  - De, Arkendra, and R. Durrett. “Spatial structure of the human population contributes to the slow decay of linkage diseqeuilibrium and shifts the site frequency spectrum.” Genetics 176 (2007): 969–81.
  - Chan, B., and R. Durrett. “A new coexistence result for competing contact processes.” Annals of Applied Probability 16, no. 3 (August 1, 2006): 1155–65. https://doi.org/10.1214/105051606000000132.
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  - Berestycki, N., and R. Durrett. “A phase transition in the random transposition random walk.” Probability Theory and Related Fields 136, no. 2 (January 1, 2006): 203–33. https://doi.org/10.1007/s00440-005-0479-7.
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  - Durrett, R. “Random graph dynamics.” Random Graph Dynamics, January 1, 2006, 1–212. https://doi.org/10.1017/CBO9780511546594.
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  - Durrett, R., and J. Schweinsberg. “Power laws for family sizes in a duplication model.” Annals of Probability 33, no. 6 (November 1, 2005): 2094–2126. https://doi.org/10.1214/009117905000000369.
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  - Durrett, R., and J. Schweinsberg. “A coalescent model for the effect of advantageous mutations on the genealogy of a population.” Stochastic Processes and Their Applications 115, no. 10 (October 1, 2005): 1628–57. https://doi.org/10.1016/j.spa.2005.04.009.
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  - Durrett, R., L. Mytnik, and E. Perkins. “Competing super-Brownian motions as limits of interacting particle systems.” Electronic Journal of Probability 10 (August 4, 2005).
  - Blasiak, J., and R. Durrett. “Random Oxford graphs.” Stochastic Processes and Their Applications 115, no. 8 (August 1, 2005): 1257–78. https://doi.org/10.1016/j.spa.2005.03.008.
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  - Schweinsberg, J., and R. Durrett. “Random partitions approximating the coalescence of lineages during a selective sweep.” Annals of Applied Probability 15, no. 3 (August 1, 2005): 1591–1651. https://doi.org/10.1214/105051605000000430.
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  - Durrett, R., and S. A. Levin. “Can stable social groups be maintained by homophilous imitation alone?.” Journal of Economic Behavior and Organization 57, no. 3 (July 1, 2005): 267–86. https://doi.org/10.1016/j.jebo.2003.09.017.
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  - York, Thomas L., Richard T. Durrett, Steven Tanksley, and Rasmus Nielsen. “Bayesian and maximum likelihood estimation of genetic maps..” Genetical Research 85, no. 2 (April 2005): 159–68. https://doi.org/10.1017/s0016672305007494.
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  - Zähle, I., J. T. Cox, and R. Durrett. “The stepping stone model. II: Genealogies and the infinite sites model.” Annals of Applied Probability 15, no. 1 B (February 1, 2005): 671–99. https://doi.org/10.1214/105051604000000701.
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  - Durrett, R., L. Mytnik, and E. Perkins. “Competing super-brownian motions as limits of interacting particle systems.” Electronic Journal of Probability 10 (January 1, 2005): 1147–1220. https://doi.org/10.1214/EJP.v10-229.
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  - Schmidt, Deena, and Rick Durrett. “Adaptive evolution drives the diversification of zinc-finger binding domains..” Molecular Biology and Evolution 21, no. 12 (December 2004): 2326–39. https://doi.org/10.1093/molbev/msh246.
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  - Durrett, Richard, and Jason Schweinsberg. “Approximating selective sweeps..” Theoretical Population Biology 66, no. 2 (September 2004): 129–38. https://doi.org/10.1016/j.tpb.2004.04.002.
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  - Sainudiin, Raazesh, Richard T. Durrett, Charles F. Aquadro, and Rasmus Nielsen. “Microsatellite mutation models: insights from a comparison of humans and chimpanzees..” Genetics 168, no. 1 (September 2004): 383–95. https://doi.org/10.1534/genetics.103.022665.
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  - Ward, Rachel, and Richard Durrett. “Subfunctionalization: How often does it occur? How long does it take?.” Theoretical Population Biology 66, no. 2 (September 2004): 93–100. https://doi.org/10.1016/j.tpb.2004.03.004.
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  - Durrett, Richard, Rasmus Nielsen, and Thomas L. York. “Bayesian estimation of genomic distance..” Genetics 166, no. 1 (January 2004): 621–29. https://doi.org/10.1534/genetics.166.1.621.
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  - Durrett, R., and V. Limic. “Rigorous results for the NK model.” Annals of Probability 31, no. 4 (October 1, 2003): 1713–53. https://doi.org/10.1214/aop/1068646364.
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  - Calabrese, Peter, and Rick Durrett. “Dinucleotide repeats in the Drosophila and human genomes have complex, length-dependent mutation processes..” Molecular Biology and Evolution 20, no. 5 (May 2003): 715–25. https://doi.org/10.1093/molbev/msg084.
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  - Cox, T., and R. Durrett. “Erratum: The stepping stone model: New formulas expose old myths (The Annals of Applied Probability (2002) 12 (1348-1377)).” Annals of Applied Probability 13, no. 2 (May 1, 2003).
  - Durrett, R. "Shuffling Chromosomes." Journal of Theoretical Probability 16, no. 3 (2003): 725-750. Full Text
  - Durrett, R., and V. Limic. “A surprising poisson process arising from a species competition model.” Stochastic Processes and Their Applications 102, no. 2 (December 1, 2002): 301–9. https://doi.org/10.1016/S0304-4149(02)00209-0.
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  - Cox, J. T., and R. Durrett. “The stepping stone model: New formulas expose old myths.” Annals of Applied Probability 12, no. 4 (November 1, 2002): 1348–77. https://doi.org/10.1214/aoap/1037125866.
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  - Buttel, Linda A., Richard Durrett, and Simon A. Levin. “Competition and species packing in patchy environments..” Theoretical Population Biology 61, no. 3 (May 2002): 265–76. https://doi.org/10.1006/tpbi.2001.1569.
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  - Durrett, R., H. Kesten, and V. Limic. “Once edge-reinforced random walk on a tree.” Probability Theory and Related Fields 122, no. 4 (April 1, 2002): 567–92. https://doi.org/10.1007/s004400100179.
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  - Balding, D. J., A. D. Carothers, J. L. Marchini, L. R. Cardon, A. Vetta, B. Griffiths, B. S. Weir, et al. “Discussion on the meeting on 'statistical modelling and analysis of genetic data'.” Journal of the Royal Statistical Society. Series B: Statistical Methodology 64, no. 4 (January 1, 2002): 737–75. https://doi.org/10.1111/1467-9868.00359.
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  - Durrett, R. “Mutual invadability implies coexistence in spatial models.” Memoirs of the American Mathematical Society, no. 740 (January 1, 2002).
  - Durrett, Richard T., Kai-Yi Chen, and Steven D. Tanksley. “A simple formula useful for positional cloning..” Genetics 160, no. 1 (January 2002): 353–55.
  - York, Thomas L., Richard Durrett, and Rasmus Nielsen. “Bayesian estimation of the number of inversions in the history of two chromosomes..” Journal of Computational Biology : A Journal of Computational Molecular Cell Biology 9, no. 6 (January 2002): 805–18. https://doi.org/10.1089/10665270260518281.
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  - Calabrese, P. P., R. T. Durrett, and C. F. Aquadro. “Dynamics of microsatellite divergence under stepwise mutation and proportional slippage/point mutation models..” Genetics 159, no. 2 (October 2001): 839–52.
  - Sundell, N. M., and R. T. Durrett. “Exponential distance statistics to detect the effects of population subdivision..” Theoretical Population Biology 60, no. 2 (September 2001): 107–16. https://doi.org/10.1006/tpbi.2001.1522.
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  - Arkendra, D. E., M. Ferguson, S. Sindi, and R. Durrett. “The equilibrium distribution for a generalized Sankoff-Ferretti model accurately predicts chromosome size distributions in a wide variety of species.” Journal of Applied Probability 38, no. 2 (June 1, 2001): 324–34. https://doi.org/10.1239/jap/996986747.
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  - Durrett, R., and V. Limic. “On the quantity and quality of single nucleotide polymorphisms in the human genome.” Stochastic Processes and Their Applications 93, no. 1 (May 1, 2001): 1–24. https://doi.org/10.1016/S0304-4149(00)00090-9.
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  - Diaconis, P, and Durrett, R. "Chutes and Ladders in Markov Chains." Journal of Theoretical Probability 14, no. 3 (2001): 899-926. Full Text
  - Broughton, R. E., S. E. Stanley, and R. T. Durrett. “Quantification of homoplasy for nucleotide transitions and transversions and a reexamination of assumptions in weighted phylogenetic analysis..” Systematic Biology 49, no. 4 (December 2000): 617–27. https://doi.org/10.1080/106351500750049734.
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  - Kruglyak, S., R. Durrett, M. D. Schug, and C. F. Aquadro. “Distribution and abundance of microsatellites in the yeast genome can Be explained by a balance between slippage events and point mutations..” Molecular Biology and Evolution 17, no. 8 (August 2000): 1210–19. https://doi.org/10.1093/oxfordjournals.molbev.a026404.
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  - Durrett, R., and S. Levin. “Lessons on pattern formation from planet WATOR..” Journal of Theoretical Biology 205, no. 2 (July 2000): 201–14. https://doi.org/10.1006/jtbi.2000.2061.
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  - Vision, T. J., D. G. Brown, D. B. Shmoys, R. T. Durrett, and S. D. Tanksley. “Selective mapping: a strategy for optimizing the construction of high-density linkage maps..” Genetics 155, no. 1 (May 2000): 407–20.
  - Liu, Y. C., R. Durrett, and M. G. Milgroom. “A spatially-structured stochastic model to simulate heterogenous transmission of viruses in fungal populations.” Ecological Modelling 127, no. 2–3 (March 30, 2000): 291–308. https://doi.org/10.1016/S0304-3800(99)00216-1.
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  - Cox, J. T., R. Durrett, and E. A. Perkins. “Rescaled voter models converge to super-Brownian motion.” Annals of Probability 28, no. 1 (January 1, 2000): 185–234. https://doi.org/10.1214/aop/1019160117.
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  - Durrett, R., L. Buttel, and R. Harrison. “Spatial models for hybrid zones..” Heredity 84 ( Pt 1) (January 2000): 9–19. https://doi.org/10.1046/j.1365-2540.2000.00566.x.
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  - Durrett, R, and Schinazi, RB. "Boundary Modified Contact Processes." Journal of Theoretical Probability 13, no. 2 (2000): 575-594.
  - Molofsky, J., R. Durrett, J. Dushoff, D. Griffeath, and S. Levin. “Local frequency dependence and global coexistence..” Theoretical Population Biology 55, no. 3 (June 1999): 270–82. https://doi.org/10.1006/tpbi.1998.1404.
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  - Durrett, R. “Stochastic spatial models.” Siam Review 41, no. 4 (January 1, 1999): 677–718. https://doi.org/10.1137/S0036144599354707.
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  - Durrett, R., and E. A. Perkins. “Rescaled contact processes converge to super-Brownian motion in two or more dimensions.” Probability Theory and Related Fields 114, no. 3 (January 1, 1999): 309–99. https://doi.org/10.1007/s004400050228.
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  - Durrett, R., and S. Kruglyak. “A new stochastic model of microsatellite evolution.” Journal of Applied Probability 36, no. 3 (January 1, 1999): 621–31. https://doi.org/10.1239/jap/1032374621.
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  - Durrett, R., and S. Kruglyak. “A new stochastic model of microsatellite evolution.” Journal of Applied Probability 36, no. 3 (January 1, 1999): 621–31. https://doi.org/10.1017/S0021900200017447.
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  - Durrett, R, Granovsky, BL, and Gueron, S. "The Equilibrium Behavior of Reversible Coagulation-Fragmentation Processes." Journal of Theoretical Probability 12, no. 2 (January 1, 1999): 447-474. Full Text
  - Kruglyak, S., R. T. Durrett, M. D. Schug, and C. F. Aquadro. “Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations..” Proceedings of the National Academy of Sciences of the United States of America 95, no. 18 (September 1998): 10774–78. https://doi.org/10.1073/pnas.95.18.10774.
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  - Bramson, M., J. T. Cox, and R. Durrett. “A spatial model for the abundance of species.” Annals of Probability 26, no. 2 (April 1, 1998): 658–709.
  - Durrett, R., and S. Levin. “Spatial aspects of interspecific competition..” Theoretical Population Biology 53, no. 1 (February 1998): 30–43. https://doi.org/10.1006/tpbi.1997.1338.
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  - Durrett, R., and S. Levin. “Erratum: Spatial aspects of interspecific competition (Theoretical Population Biology (1998) 53:1 (30-43)).” Theoretical Population Biology 53, no. 3 (January 1, 1998). https://doi.org/10.1006/tpbi.1998.1374.
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  - Durrett, R., and S. Levin. “Allelopathy in spatially distributed populations.” Journal of Theoretical Biology 185, no. 2 (March 21, 1997): 165–71. https://doi.org/10.1006/jtbi.1996.0292.
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  - Chen, Z. Q., R. Durrett, and G. Ma. “Holomorphic diffusions and boundary behavior of harmonic functions.” Annals of Probability 25, no. 3 (January 1, 1997): 1103–34. https://doi.org/10.1214/aop/1024404507.
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  - Durrett, R., and C. Neuhauser. “Coexistence results for some competition models.” Annals of Applied Probability 7, no. 1 (January 1, 1997): 10–45. https://doi.org/10.1214/aoap/1034625251.
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  - Allouba, H, Durrett, R, Hawkes, J, and Perkins, E. "Super-Tree Random Measures." Journal of Theoretical Probability 10, no. 3 (1997): 773-794.
  - Durrett, R., and S. Levin. “Spatial models for species-area curves.” Journal of Theoretical Biology 179, no. 2 (March 14, 1996): 119–27. https://doi.org/10.1006/jtbi.1996.0053.
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  - Bramson, M., J. T. Cox, and R. Durrett. “Spatial models for species area curves.” Annals of Probability 24, no. 4 (January 1, 1996): 1727–51. https://doi.org/10.1214/aop/1041903204.
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  - Cox, J. T., and R. Durrett. “Hybrid zones and voter model interfaces.” Bernoulli 1, no. 4 (January 1, 1995): 343–70. https://doi.org/10.3150/bj/1193758711.
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  - Durrett, R., and G. Swindle. “Coexistence results for catalysts.” Probability Theory and Related Fields 98, no. 4 (December 1, 1994): 489–515. https://doi.org/10.1007/BF01192836.
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  - Durrett, R., and S. A. Levin. “Stochastic spatial models: A user's guide to ecological applications.” Philosophical Transactions of the Royal Society B: Biological Sciences 343, no. 1305 (January 1, 1994): 329–50. https://doi.org/10.1098/rstb.1994.0028.
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  - Durrett, R., and S. Levin. “The importance of being discrete (and spatial).” Theoretical Population Biology 46, no. 3 (January 1, 1994): 363–94. https://doi.org/10.1006/tpbi.1994.1032.
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  - Durrett, R., and D. Griffeath. “Asymptotic behavior of excitable cellular automata.” Experimental Mathematics 2, no. 3 (January 1, 1993): 183–208. https://doi.org/10.1080/10586458.1993.10504277.
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  - Durrett, R. T., and L. C. G. Rogers. “Asymptotic behavior of Brownian polymers.” Probability Theory and Related Fields 92, no. 3 (September 1, 1992): 337–49. https://doi.org/10.1007/BF01300560.
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  - Durrett, R. “Multicolor particle systems with large threshold and range.” Journal of Theoretical Probability 5, no. 1 (January 1, 1992): 127–52. https://doi.org/10.1007/BF01046781.
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  - Durrett, R., and J. E. Steif. “Some rigorous results for the Greenberg-Hastings Model.” Journal of Theoretical Probability 4, no. 4 (October 1, 1991): 669–90. https://doi.org/10.1007/BF01259549.
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  - Cox, J. T., R. Durrett, and R. Schinazi. “The critical contact process seen from the right edge.” Probability Theory and Related Fields 87, no. 3 (September 1, 1991): 325–32. https://doi.org/10.1007/BF01312213.
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  - Durrett, R., and A. M. Møller. “Complete convergence theorem for a competition model.” Probability Theory and Related Fields 88, no. 1 (March 1, 1991): 121–36. https://doi.org/10.1007/BF01193585.
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  - Bramson, M., D. Wan-ding, and R. Durrett. “Annihilating branching processes.” Stochastic Processes and Their Applications 37, no. 1 (January 1, 1991): 1–17. https://doi.org/10.1016/0304-4149(91)90056-I.
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  - Durrett, R., H. Kesten, and E. Waymire. “On weighted heights of random trees.” Journal of Theoretical Probability 4, no. 1 (January 1, 1991): 223–37. https://doi.org/10.1007/BF01047004.
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  - Durrett, R., and G. Swindle. “Are there bushes in a forest?.” Stochastic Processes and Their Applications 37, no. 1 (January 1, 1991): 19–31. https://doi.org/10.1016/0304-4149(91)90057-J.
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  - Jinwen, C., R. Durrett, and L. Xiufang. “Exponential convergence for one dimensional contact processes.” Acta Mathematica Sinica 6, no. 4 (December 1, 1990): 349–53. https://doi.org/10.1007/BF02107968.
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  - Cox, J. T., and R. Durrett. “Large deviations for independent random walks.” Probability Theory and Related Fields 84, no. 1 (March 1, 1990): 67–82. https://doi.org/10.1007/BF01288559.
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  - Ding, W. D., R. Durrett, and T. M. Liggett. “Ergodicity of reversible reaction diffusion processes.” Probability Theory and Related Fields 85, no. 1 (March 1, 1990): 13–26. https://doi.org/10.1007/BF01377624.
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  - Durrett, R., R. H. Schonmann, and N. I. Tanaka. “Correlation lengths for oriented percolation.” Journal of Statistical Physics 55, no. 5–6 (June 1, 1989): 965–79. https://doi.org/10.1007/BF01041074.
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  - Durrett, R., and N. I. Tanaka. “Scaling inequalities for oriented percolation.” Journal of Statistical Physics 55, no. 5–6 (June 1, 1989): 981–95. https://doi.org/10.1007/BF01041075.
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  - Bramson, M., and R. Durrett. “A simple proof of the stability criterion of Gray and Griffeath.” Probability Theory and Related Fields 80, no. 2 (December 1, 1988): 293–98. https://doi.org/10.1007/BF00356107.
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  - Durrett, R., and R. H. Schonmann. “Large deviations for the contact process and two dimensional percolation.” Probability Theory and Related Fields 77, no. 4 (December 1, 1988): 583–603. https://doi.org/10.1007/BF00959619.
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  - Bramson, M., and R. Durrett. “Random walk in random environment: A counterexample?.” Communications in Mathematical Physics 119, no. 2 (June 1, 1988): 199–211. https://doi.org/10.1007/BF01217738.
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  - Durrett, R. “Crabgrass, measles, and gypsy moths: An introduction to interacting particle systems.” The Mathematical Intelligencer 10, no. 2 (June 1, 1988): 37–47. https://doi.org/10.1007/BF03028355.
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  - Chayes, J. T., L. Chayes, and R. Durrett. “Connectivity properties of Mandelbrot's percolation process.” Probability Theory and Related Fields 77, no. 3 (March 1, 1988): 307–24. https://doi.org/10.1007/BF00319291.
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  - Cox, J. T., and R. Durrett. “Limit theorems for the spread of epidemics and forest fires.” Stochastic Processes and Their Applications 30, no. 2 (January 1, 1988): 171–91. https://doi.org/10.1016/0304-4149(88)90083-X.
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  - Durrett, R. “Crabgrass, measles, and gypsy moths: An introduction to modern probability.” Bulletin of the American Mathematical Society 18, no. 2 (January 1, 1988): 117–43. https://doi.org/10.1090/S0273-0979-1988-15625-X.
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  - Chayes, J. T., L. Chayes, and R. Durrett. “Inhomogeneous percolation problems and incipient infinite clusters.” Journal of Physics A: Mathematical and General 20, no. 6 (December 1, 1987): 1521–30. https://doi.org/10.1088/0305-4470/20/6/034.
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  - Brennan, M. D., and R. Durrett. “Splitting intervals II: Limit laws for lengths.” Probability Theory and Related Fields 75, no. 1 (May 1, 1987): 109–27. https://doi.org/10.1007/BF00320085.
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  - Chayes, J. T., L. Chayes, and R. Durrett. “Critical behavior of the two-dimensional first passage time.” Journal of Statistical Physics 45, no. 5–6 (December 1, 1986): 933–51. https://doi.org/10.1007/BF01020583.
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  - Durrett, R. “Multidimensional random walks in random environments with subclassical limiting behavior.” Communications in Mathematical Physics 104, no. 1 (March 1, 1986): 87–102. https://doi.org/10.1007/BF01210794.
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  - Durrett, R. “Some general results concerning the critical exponents of percolation processes.” Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 69, no. 3 (September 1, 1985): 421–37. https://doi.org/10.1007/BF00532742.
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  - Durrett, R., and B. Nguyen. “Thermodynamic inequalities for percolation.” Communications in Mathematical Physics 99, no. 2 (June 1, 1985): 253–69. https://doi.org/10.1007/BF01212282.
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  - Durrett, R., and T. M. Liggett. “Fixed points of the smoothing transformation.” Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 64, no. 3 (September 1, 1983): 275–301. https://doi.org/10.1007/BF00532962.
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  - Durrett, R. “Maxima of branching random walks.” Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 62, no. 2 (June 1, 1983): 165–70. https://doi.org/10.1007/BF00538794.
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  - Chung, K. L., R. Durrett, and Z. Zhao. “Extension of domains with finite gauge.” Mathematische Annalen 264, no. 1 (March 1, 1983): 73–79. https://doi.org/10.1007/BF01458051.
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  - Cox, J. T., and R. Durrett. “Oriented Percolation in Dimensions D ≥ 4: Bounds and Asymptotic Formulas.” Mathematical Proceedings of the Cambridge Philosophical Society 93, no. 1 (January 1, 1983): 151–62. https://doi.org/10.1017/S0305004100060436.
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  - Durrett, R., and D. Griffeath. “Contact processes in several dimensions.” Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 59, no. 4 (December 1, 1982): 535–52. https://doi.org/10.1007/BF00532808.
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  - Durrett, R. “An introduction to infinite particle systems.” Stochastic Processes and Their Applications 11, no. 2 (January 1, 1981): 109–50. https://doi.org/10.1016/0304-4149(81)90001-6.
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  - Durrett, R. “Conditioned limit theorems for random walks with negative drift.” Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 52, no. 3 (January 1, 1980): 277–87. https://doi.org/10.1007/BF00538892.
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  - Anthony, P. F., R. Durrett, J. L. Pulec, and J. L. Hartstone. “A new parameter in brain stem evoked response: component wave areas..” The Laryngoscope 89, no. 10 Pt 1 (October 1979): 1569–78. https://doi.org/10.1002/lary.5540891004.
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  - Anthony, P. F., R. Durrett, J. L. Pulec, and J. L. Hartstone. “A new parameter in brain stem evoked response: Component wave areas.” Laryngoscope 89, no. 10 I (1979): 1569–78.
  - Durrett, R. “Maxima of branching random walks vs. independent random walks.” Stochastic Processes and Their Applications 9, no. 2 (January 1, 1979): 117–35. https://doi.org/10.1016/0304-4149(79)90024-3.
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  - Durrett, R. “The genealogy of critical branching processes.” Stochastic Processes and Their Applications 8, no. 1 (January 1, 1978): 101–16. https://doi.org/10.1016/0304-4149(78)90071-6.
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  - Durrett, R. T., and S. I. Resnick. “Weak convergence with random indices.” Stochastic Processes and Their Applications 5, no. 3 (January 1, 1977): 213–20. https://doi.org/10.1016/0304-4149(77)90031-X.
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  - Chung, K. L., and R. Durrett. “Downcrossings and local time.” Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 35, no. 2 (June 1, 1976): 147–49. https://doi.org/10.1007/BF00533319.
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  - Durrett, R. T., and S. G. Ghurye. “WAITING TIMES WITHOUT MEMORY..” J Appl Probab 13, no. 1 (January 1, 1976): 65–75.
  - Durrett, R. T., and C. Varghese. “Evolving spatial networks to minimize length.” Journal of Complex Networks 3, no. 3 (n.d.): 411–30. https://doi.org/10.1093/comet/cnu044.
    Full Text Link to Item
  - Durrett, R. T., and D. Sivakoff. “Two evolving social network models.” Alea (Rio De Janeiro): Latin American Journal of Probability and Mathematical Statistics XII, no. 2 (n.d.): 699–715.
    Open Access Copy
- Book Sections
  - Chung, K. L., and R. Durrett. “Downcrossings and local time.” In Selected Works of Kai Lai Chung, 585–87, 2008. https://doi.org/10.1142/9789812833860_0037.
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