A long-range contact process in a random environment

2023/10/18 by Jahnel, Benedikt, Vu, Anh Duc · 1 citation
#60K35 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2310.12061

Abstract

We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited at random times. We prove a phase transition in the recovery parameter via block arguments. This contributes to a line of research on directed percolation with long-range correlations in nonstabilizing random environments.

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• Oriented bond-site percolation in random environment and contact processes with periodic recovery

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