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The entirely coupled region of supercritical contact processes

Published online by Cambridge University Press:  24 October 2016

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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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