The survival of large dimensional threshold contact processes

Details The survival of large dimensional threshold contact processes The survival of large dimensional threshold contact processes

2009-08-28

arxiv.org/abs/0908.4146v1

Annals of Probability 2009, Vol. 37, No. 4, 1483-1501

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AOP440 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/08-AOP440

We study the threshold $\theta$ contact process on $\mathbb{Z}^d$ with infection parameter $\lambda$. We show that the critical point $\lambda_{\mathrm{c}}$, defined as the threshold for survival starting from every site occupied, vanishes as $d\to\infty$. This implies that the threshold $\theta$ voter model on $\mathbb{Z}^d$ has a nondegenerate extremal invariant measure, when $d$ is large.

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