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July 2009 The survival of large dimensional threshold contact processes
Thomas Mountford, Roberto H. Schonmann
Ann. Probab. 37(4): 1483-1501 (July 2009). DOI: 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.

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Thomas Mountford. Roberto H. Schonmann. "The survival of large dimensional threshold contact processes." Ann. Probab. 37 (4) 1483 - 1501, July 2009. https://doi.org/10.1214/08-AOP440

Information

Published: July 2009
First available in Project Euclid: 21 July 2009

zbMATH: 1172.60032
MathSciNet: MR2546752
Digital Object Identifier: 10.1214/08-AOP440

Subjects:
Primary: 60K35

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 4 • July 2009
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