The Annals of Probability

The survival of large dimensional threshold contact processes

Thomas Mountford and Roberto H. Schonmann

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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.

Article information

Source
Ann. Probab., Volume 37, Number 4 (2009), 1483-1501.

Dates
First available in Project Euclid: 21 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1248182145

Digital Object Identifier
doi:10.1214/08-AOP440

Mathematical Reviews number (MathSciNet)
MR2546752

Zentralblatt MATH identifier
1172.60032

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Threshold contact process threshold voter model critical points invariant measures large dimensions

Citation

Mountford, Thomas; Schonmann, Roberto H. The survival of large dimensional threshold contact processes. Ann. Probab. 37 (2009), no. 4, 1483--1501. doi:10.1214/08-AOP440. https://projecteuclid.org/euclid.aop/1248182145


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