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The symbiotic contact process

Publication ,  Journal Article
Durrett, R; Yao, D
Published in: Electronic Journal of Probability
January 1, 2020

We consider a contact process on Zd with two species that interact in a symbiotic manner. Each site can either be vacant or occupied by individuals of species A and/or B. Multiple occupancy by the same species at a single site is prohibited. The name symbiotic comes from the fact that if only one species is present at a site then that particle dies with rate 1 but if both species are present then the death rate is reduced to µ ≤ 1 for each particle at that site. We show the critical birth rate λc(µ) for weak survival is of order√µ as µ → 0. Mean-field calculations predict that when µ < 1/2 there is a discontinuous transition as λ is varied. In contrast, we show that, in any dimension, the phase transition is continuous. To be fair to the physicists that introduced the model, [27], the authors say that the symbiotic contact process is in the directed percolation universality class and hence has a continuous transition. However, a 2018 paper, [30], asserts that the transition is discontinuous above the upper critical dimension, which is 4 for oriented percolation.

Duke Scholars

Published In

Electronic Journal of Probability

DOI

EISSN

1083-6489

Publication Date

January 1, 2020

Volume

25

Related Subject Headings

  • Statistics & Probability
  • 0105 Mathematical Physics
  • 0104 Statistics
 

Citation

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Durrett, R., & Yao, D. (2020). The symbiotic contact process. Electronic Journal of Probability, 25. https://doi.org/10.1214/19-EJP402
Durrett, R., and D. Yao. “The symbiotic contact process.” Electronic Journal of Probability 25 (January 1, 2020). https://doi.org/10.1214/19-EJP402.
Durrett R, Yao D. The symbiotic contact process. Electronic Journal of Probability. 2020 Jan 1;25.
Durrett, R., and D. Yao. “The symbiotic contact process.” Electronic Journal of Probability, vol. 25, Jan. 2020. Scopus, doi:10.1214/19-EJP402.
Durrett R, Yao D. The symbiotic contact process. Electronic Journal of Probability. 2020 Jan 1;25.

Published In

Electronic Journal of Probability

DOI

EISSN

1083-6489

Publication Date

January 1, 2020

Volume

25

Related Subject Headings

  • Statistics & Probability
  • 0105 Mathematical Physics
  • 0104 Statistics