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A long-range contact process in a random environment

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arxiv 2310.12061 v1 pith:JXH3XIYH submitted 2023-10-18 math.PR

Benedikt Jahnel , Anh Duc Vu This is my paper · ORCID
classification math.PR
keywords long-rangerandominfectionprocessaccordingargumentsblockcontact
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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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  1. Oriented bond-site percolation in random environment and contact processes with periodic recovery

    math.PR 2025-06 conditional novelty 7.0 of 10

    For oriented bond-site percolation with columnar stretches, a (1+ε)-moment condition on stretches suffices for a percolation phase transition, yielding survival of contact processes with periodic recovery.

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