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The contact process with fast voting

Publication ,  Journal Article
Durrett, R; Liggett, T; Zhang, Y
Published in: Electronic Journal of Probability
March 3, 2014

Consider a combination of the contact process and the voter model in which deaths occur at rate 1 per site, and across each edge between nearest neighbors births occur at rate λ and voting events occur at rate θ. We are interested in the asymptotics as θ→∞ of the critical value λc(θ) for the existence of a nontrivial stationary distribution. In d≥3, λc(θ)→1/(2dρd) where ρd is the probability a d dimensional simple random walk does not return to its starting point.In d=2, λc(θ)/log(θ)→1/4π, while in d=1, λc(θ)/θ1/2 has lim inf≥1/2√ and lim sup<∞.The lower bound might be the right answer, but proving this, or even getting a reasonable upper bound, seems to be a difficult problem.

Duke Scholars

Published In

Electronic Journal of Probability

DOI

EISSN

1083-6489

Publication Date

March 3, 2014

Volume

19

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0105 Mathematical Physics
  • 0104 Statistics
 

Citation

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MLA
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Durrett, R., Liggett, T., & Zhang, Y. (2014). The contact process with fast voting. Electronic Journal of Probability, 19. https://doi.org/10.1214/EJP.v19-3021
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.
Durrett R, Liggett T, Zhang Y. The contact process with fast voting. Electronic Journal of Probability. 2014 Mar 3;19.
Durrett, R., et al. “The contact process with fast voting.” Electronic Journal of Probability, vol. 19, Mar. 2014. Scopus, doi:10.1214/EJP.v19-3021.
Durrett R, Liggett T, Zhang Y. The contact process with fast voting. Electronic Journal of Probability. 2014 Mar 3;19.

Published In

Electronic Journal of Probability

DOI

EISSN

1083-6489

Publication Date

March 3, 2014

Volume

19

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0105 Mathematical Physics
  • 0104 Statistics