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Coexistence in chase-escape

Publication ,  Journal Article
Durrett, R; Junge, M; Tang, S
Published in: Electronic Communications in Probability
January 1, 2020

We study a competitive stochastic growth model called chase-escape in which red particles spread to adjacent uncolored sites and blue particles only to adjacent red sites. Red particles are killed when blue occupies the same site. If blue has rate-1 passage times and red rate-λ, a phase transition occurs for the probability red escapes to infinity on ℤd, d-ary trees, and the ladder graph ℤ X {0, 1}. The result on the tree was known, but we provide a new, simpler calculation of the critical value, and observe that it is a lower bound for a variety of graphs. We conclude by showing that red can be stochastically slower than blue, but still escape with positive probability for large enough d on oriented ℤd with passage times that resemble Bernoulli bond percolation.

Duke Scholars

Published In

Electronic Communications in Probability

DOI

EISSN

1083-589X

Publication Date

January 1, 2020

Volume

25

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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Durrett, R., Junge, M., & Tang, S. (2020). Coexistence in chase-escape. Electronic Communications in Probability, 25. https://doi.org/10.1214/20-ECP302
Durrett, R., M. Junge, and S. Tang. “Coexistence in chase-escape.” Electronic Communications in Probability 25 (January 1, 2020). https://doi.org/10.1214/20-ECP302.
Durrett R, Junge M, Tang S. Coexistence in chase-escape. Electronic Communications in Probability. 2020 Jan 1;25.
Durrett, R., et al. “Coexistence in chase-escape.” Electronic Communications in Probability, vol. 25, Jan. 2020. Scopus, doi:10.1214/20-ECP302.
Durrett R, Junge M, Tang S. Coexistence in chase-escape. Electronic Communications in Probability. 2020 Jan 1;25.

Published In

Electronic Communications in Probability

DOI

EISSN

1083-589X

Publication Date

January 1, 2020

Volume

25

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics