Survival of Threshold Contact Processes

Shirin J. Handjani ()
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Shirin J. Handjani: University of Colorado

Journal of Theoretical Probability, 1997, vol. 10, issue 3, 737-746

Abstract: Abstract We consider the d-dimensional threshold contact process. Suppose that a vacant site becomes occupied at rate one when there are at least θ occupied sites in its neighborhood, and the death rate at any site is δ>0. We will explicitly give two integers a≤b with the following properties: For θ≤a the process survives starting from finite configurations when δ is small, but for θ>a the process dies out starting from any finite configuration with any positive death rate. For θ≤b the process has a nontrivial invariant measure when δ is small, but for θ>b the only invariant measure is the all-zero configuration for any positive death rate.

Keywords: Particle systems; threshold contact; finite survival; infinite survival (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022609912993

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