Unusual properties of contact processes on percolated graphs

2024/03/27 by Rick Durrett, Durrett, Rick · 1 citation
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2403.18592

openalex publication_date 2024/03/27 · openalex created_date 2024/03/29 · openalex updated_date 2026/07/28

Abstract

In this paper we will consider the contact process in a very simple type of random environment that physicists call the random dilution model. We start with the contact process on a graph, here either ℤ^d, a d-dimensional torus or an \ER graph, and then flip independent (1-p) coins to delete edges, or delete vertices. Let p^* be the threshold for percolation in the diluted graph. We will primarily be concerned with two phenomena. (i) The critical value for the contact process on the dliuted graph λ_c(p) does not converge to ∞ as p \downarrow p^*. (ii) In contrast to the contact process on a homogeneous graph, the density of 1's starting from all sites occupied converges to 0 at a polynomial rate when p

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• Phase transitions for contact processes on sparse random graphs via metastability and local limits

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