The survival of large dimensional threshold contact processes

Thomas Mountford, Roberto H. Schonmann

Type: Article

Publication Date: 2009-07-01

Citations: 8

DOI: https://doi.org/10.1214/08-aop440

Abstract

We study the threshold θ contact process on ℤd with infection parameter λ. We show that the critical point λc, defined as the threshold for survival starting from every site occupied, vanishes as d→∞. This implies that the threshold θ voter model on ℤd has a nondegenerate extremal invariant measure, when d is large.

Locations

The Annals of Probability - View - PDF
arXiv (Cornell University) - View - PDF
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