The contact process with fast voting


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Liggett, T; Zhang, Y

Published Date

  • March 3, 2014

Published In

Volume / Issue

  • 19 /

Electronic International Standard Serial Number (EISSN)

  • 1083-6489

Digital Object Identifier (DOI)

  • 10.1214/EJP.v19-3021

Citation Source

  • Scopus