Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., University of Rochester 1988
  • M.Sc., Chinese Academy of Sciences (China) 1982
• 

  Duke Appointment History

  • Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1999 - 2014
  • Associate Professor with Tenure, Mathematics, Trinity College of Arts & Sciences 1995 - 1999
  • Associate Professor, Mathematics, Trinity College of Arts & Sciences 1993 - 1995
• Recognition
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  Awards & Honors

  • Fellowship. John Simon Guggenheim Memorial Foundation. 1999
  • George Polya Prize. Society for Industrial and Applied Mathematics. 1998
• Research
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  Selected Grants

  • Riemann-Hilbert Problem and Integrable Systems awarded by  National Science Foundation 2006 - 2010
  • Riemann-Hilbert problem and integrable systems awarded by  National Science Foundation 2003 - 2007
  • Inverse Scattering Theory awarded by  National Science Foundation 2000 - 2003
  • (97-0380) Inverse Scattering Theory awarded by  National Science Foundation 1997 - 2000
  • (94-0255) Inverse Scattering Theory awarded by  National Science Foundation 1994 - 1997
• Publications & Artistic Works
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  Selected Publications

  • Academic Articles

    • Rider, B., and X. Zhou. “Janossy densities for unitary ensembles at the spectral edge.” International Mathematics Research Notices 2008, no. 1 (December 1, 2008). https://doi.org/10.1093/imrn/rnn037.
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    • McLaughlin, K. T. R., A. H. Vartanian, and X. Zhou. “Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I.” Mathematical Physics Analysis and Geometry 11, no. 3–4 (November 1, 2008): 187–364. https://doi.org/10.1007/s11040-008-9042-y.
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    • McLaughlin, K. T. R., A. H. Vartanian, and X. Zhou. “Asymptotics of laurent polynomials of odd degree orthogonal with respect to varying exponential weights.” Constructive Approximation 27, no. 2 (March 1, 2008): 149–202. https://doi.org/10.1007/s00365-007-0675-z.
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    • McLaughlin, K. T. -. R., and A. H. Vartanian. “Asymptotics of Coefficients of Recurrence Relations, Hankel Determinants Ratios, and Root Products Associated with Orthogonal Laurent Polynomials with Respect to Varying Exponential Weights.” Journal Acta Applicandae Mathematicae 100 (2008): 39–104.
    • McLaughlin, K. T. R., A. H. Vartanian, and X. Zhou. “Asymptotics of recurrence relation coefficients, hankel determinant ratios, and root products associated with laurent polynomials orthogonal with respect to varying exponential weights.” Acta Applicandae Mathematicae 100, no. 1 (January 1, 2008): 39–104. https://doi.org/10.1007/s10440-007-9176-0.
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    • Tovbis, A., S. Venakides, and X. Zhou. “Semiclassical focusing nonlinear schrödinger equation i: Inverse scattering map and its evolution for radiative initial data.” International Mathematics Research Notices 2007 (December 1, 2007). https://doi.org/10.1093/imrn/rnm094.
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    • Deift, P., A. Its, I. Krasovsky, and X. Zhou. “The Widom-Dyson constant for the gap probability in random matrix theory.” Journal of Computational and Applied Mathematics 202, no. 1 SPECIAL ISSUE (May 1, 2007): 26–47. https://doi.org/10.1016/j.cam.2005.12.040.
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    • McLaughlin, K. T. R., A. H. Vartanian, and X. Zhou. “Asymptotics of Laurent polynomials of even degree orthogonal with respect to varying exponential weights.” International Mathematics Research Papers 2006 (October 18, 2006). https://doi.org/10.1155/IMRP/2006/62815.
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    • Deift, P., A. Its, and I. Krasovsky. “The Widpm-Dyson constant for the gap probability in random matrix theory.” A Special Edition of the Journal of  Computational and Applied Mathematics, 2006.
    • McLaughlin, K. T. -. R., and A. H. Vartanian. “Asymptotics of Orthogonal Laurent Polynomials of Even Degree with Respect to Varying Exponential Weights.” Imrn, 2006.
    • Tovbis, A., S. Venakides, and X. Zhou. “On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case.” Communications on Pure and Applied Mathematics 59, no. 10 (January 1, 2006): 1379–1432. https://doi.org/10.1002/cpa.20142.
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    • Tovbis, A., S. Venakides, and X. Zhou. “On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation.” Communications on Pure and Applied Mathematics 57, no. 7 (July 1, 2004): 877–985. https://doi.org/10.1002/cpa.20024.
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    • Deift, P., and X. Zhou. “Long-Time Asymptotics for Solutions of the NLS Equation with Initial Data in a Weighted Sobolev Space.” Communications on Pure and Applied Mathematics 56, no. 8 (August 1, 2003): 1029–77. https://doi.org/10.1002/cpa.3034.
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    • Deift, P. “Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space.” Comm. Pure Appl. Math. 56 (2003): 1–49.
    • Deift, P., and X. Zhou. “A priori L^p-estimates for solutions of Riemann-Hilbert problems.” International Mathematics Research Notices, no. 40 (December 3, 2002): 2121–54.
    • Liu, W. M., B. Wu, X. Zhou, D. K. Campbell, S. T. Chui, and Q. Niu. “Interacting domain walls in an easy-plane ferromagnet.” Physical Review B  Condensed Matter and Materials Physics 65, no. 17 (May 1, 2002): 1724161–64. https://doi.org/10.1103/PhysRevB.65.172416.
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    • Deift, P. “Uniform L^p estimates for solutions of Riemann--Hilbert Problems depending on external parameters.” Intl. Math. Res. Notices, no. 40 (2002): 2121–54.
    • Deift, P., and X. Zhou. “Perturbation theory for infinite-dimensional integrable systems on the line. A case study.” Acta Mathematica 188, no. 2 (January 1, 2002): 163–262. https://doi.org/10.1007/BF02392683.
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    • Baik, J., P. Deift, K. McLaughlin, P. Miller, and X. Zhou. “Optimal tail estimates for directed last passage site percolation with geometric random variables.” Advances in Theoretical and Mathematical Physics 5, no. 6 (November 1, 2001): 1–41.
    • Deift, P., T. Kriecherbauer, K. R. McLaughlin, S. Venakides, and X. Zhou. “A riemann-Hilbert approach to asymptotic questions for orthogonal polynomials.” Journal of Computational and Applied Mathematics 133, no. 1–2 (August 1, 2001): 47–63. https://doi.org/10.1016/S0377-0427(00)00634-8.
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    • Baik, J., P. Deift, K. T. R. McLaughlin, and P. Miller. “Optimal tail estimates for directed last passage site percolation with geometric random variables.” Adv. Theo. Math. Phys. 5, no. 6 (2001): 1207–50.
    • Cheng, P. J., S. Venakides, and X. Zhou. “Long-time asymptotics for the pure radiation solution of the sine-Gordon equation.” Communications in Partial Differential Equations 24, no. 7–8 (January 1, 1999): 1195–1262. https://doi.org/10.1080/03605309908821464.
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    • Deift, P., A. Its, A. Kapaev, and X. Zhou. “On the algebro-geometric integration of the Schlesinger equations.” Communications in Mathematical Physics 203, no. 3 (January 1, 1999): 613–33. https://doi.org/10.1007/s002200050037.
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    • Deift, P., T. Kriecherbauer, K. T. R. McLaughlin, S. Venakides, and X. Zhou. “Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory.” Communications on Pure and Applied Mathematics 52, no. 11 (January 1, 1999): 1335–1425. https://doi.org/10.1002/(SICI)1097-0312(199911)52:11<1335::AID-CPA1>3.0.CO;2-1.
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    • Deift, P., T. Kriecherbauer, K. T. R. Mclaughlin, S. Venakides, and X. Zhou. “Strong asymptotics of orthogonal polynomials with respect to exponential weights.” Communications on Pure and Applied Mathematics 52, no. 12 (January 1, 1999): 1491–1552. https://doi.org/10.1002/(SICI)1097-0312(199912)52:12<1491::AID-CPA2>3.0.CO;2-#.
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    • Liu, W. M., W. S. Zhang, F. C. Pu, and X. Zhou. “Nonlinear magnetization dynamics of the classical ferromagnet with two single-ion anisotropies in an external magnetic field.” Physical Review B  Condensed Matter and Materials Physics 60, no. 18 (January 1, 1999): 12893–911. https://doi.org/10.1103/PhysRevB.60.12893.
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    • Deift, P., S. Venakides, and X. Zhou. “An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation..” Proceedings of the National Academy of Sciences of the United States of America 95, no. 2 (January 1998): 450–54. https://doi.org/10.1073/pnas.95.2.450.
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    • Zhou, X. “L²-Sobolev space bijectivity of the scattering and inverse scattering transforms.” Communications on Pure and Applied Mathematics 51, no. 7 (January 1, 1998). https://doi.org/10.1002/(SICI)1097-0312(199807)51:7<697::AID-CPA1>3.0.CO;2-1.
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    • Zhou, X. “L²-Sobolev space bijectivity of the scattering and inverse scattering transforms.” Communications on Pure and Applied Mathematics 51, no. 7 (1998): X–730.
    • Deift, P., S. Venakides, and X. Zhou. “New Results in Small Dispersion KdV by an Extension of the Steepest Descent Method for Riemann-Hilbert Problems.” International Mathematics Research Notices, no. 6 (December 1, 1997): 284–99.
    • Deift, P., T. Kriecherbauer, K. T. R. McLaughlin, S. Venakides, and X. Zhou. “Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights.” International Mathematics Research Notices, no. 16 (December 1, 1997).
    • Zhou, X. “Strong regularizing effect of integrable systems.” Communications in Partial Differential Equations 22, no. 3–4 (December 1, 1997): 503–26.
    • Deift, P. A., A. R. Its, and X. Zhou. “A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics.” Annals of Mathematics 146, no. 1 (January 1, 1997): 149–235. https://doi.org/10.2307/2951834.
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    • Deift, P., and X. Zhou. “Near integrable systems on the line. A case study-pertubation theory of the defocusing nonlinear Schrödinger equation.” Mathematical Research Letters 4, no. 5 (January 1, 1997): 761–72. https://doi.org/10.4310/MRL.1997.v4.n5.a13.
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    • Deift, P., S. Kamvissis, T. Kriecherbauer, and X. Zhou. “The toda rarefaction problem.” Communications on Pure and Applied Mathematics 49, no. 1 (January 1, 1996): 35–83. https://doi.org/10.1002/(SICI)1097-0312(199601)49:1<35::AID-CPA2>3.0.CO;2-8.
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    • Xin, X. “Inverse scattering transform for systems with rational spectral dependence.” Journal of Differential Equations 115, no. 2 (January 20, 1995): 277–303. https://doi.org/10.1006/jdeq.1995.1015.
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    • Deift, P. A., and X. Zhou. “Asymptotics for the painlevé II equation.” Communications on Pure and Applied Mathematics 48, no. 3 (January 1, 1995): 277–337. https://doi.org/10.1002/cpa.3160480304.
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    • Deift, P. A., and X. Zhou. “Long-time asymptotics for integrable systems. Higher order theory.” Communications in Mathematical Physics 165, no. 1 (October 1, 1994): 175–91. https://doi.org/10.1007/BF02099741.
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    • Deift, P., S. Venakides, and X. Zhou. “The collisionless shock region for the long‐time behavior of solutions of the KdV equation.” Communications on Pure and Applied Mathematics 47, no. 2 (January 1, 1994): 199–206. https://doi.org/10.1002/cpa.3160470204.
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    • Fokas, A. S., U. Mugan, and X. Zhou. “On the solvability of Painleve I, III and V.” Inverse Problems 8, no. 5 (December 1, 1992): 757–85. https://doi.org/10.1088/0266-5611/8/5/006.
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    • Fokas, A. S., and X. Zhou. “On the solvability of Painlevé II and IV.” Communications in Mathematical Physics 144, no. 3 (March 1, 1992): 601–22. https://doi.org/10.1007/BF02099185.
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    • Deift, P., and X. Zhou. “A steepest descent method for oscillatory Riemann-Hilbert problems.” Bulletin of the American Mathematical Society 26, no. 1 (January 1, 1992): 119–23. https://doi.org/10.1090/S0273-0979-1992-00253-7.
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    • Deift, P., and X. Zhou. “Direct and inverse scattering on the line with arbitrary singularities.” Communications on Pure and Applied Mathematics 44, no. 5 (January 1, 1991): 485–533. https://doi.org/10.1002/cpa.3160440502.
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    • Zhou, X. “Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation.” Communications in Mathematical Physics 128, no. 3 (March 1, 1990): 551–64. https://doi.org/10.1007/BF02096873.
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    • Zhou, X. “Direct and inverse scattering transforms with arbitrary spectral singularities.” Communications on Pure and Applied Mathematics 42, no. 7 (January 1, 1989): 895–938. https://doi.org/10.1002/cpa.3160420702.
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