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The entirely coupled region of supercritical contact processes

Part of: Special processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  24 October 2016

Achillefs Tzioufas
Achillefs Tzioufas*
Affiliation:
Universidad de Buenos Aires
*
* Current address: Instituto de Matemática e Estatística - USP, Rua do Matão, 1010, CEP 05508-900 São Paulo, Brasil. Email address: tzioufas@ime.usp.br
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Abstract

We consider translation-invariant, finite-range, supercritical contact processes. We show the existence of unbounded space-time cones within which the descendancy of the process from full occupancy may with positive probability be identical to that of the process from the single site at its apex. The proof comprises an argument that leans upon refinements of a successful coupling among these two processes, and is valid in d-dimensions.

Keywords

Contact processesasymptotic shape theoremcouplingfinite rangecoupling eventcoupling time

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82C43: Time-dependent percolation
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 925 - 929
Copyright
Copyright © Applied Probability Trust 2016 

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