Metastable Densities for Contact Processes on Power Law Random Graphs

2011/06/21 by Thomas Mountford, Mountford, Thomas, Daniel Valesin +3 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1106.4336

36 pages; complete revision

openalex publication_date 2011/06/21 · arxiv created 2012/12/07 · arxiv updated 2012/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett, who showed that for arbitrarily small infection parameter λ, the survival time of the process is larger than a stretched exponential function of the number of vertices, n. We obtain sharp bounds for the typical density of infected sites in the graph, as λ is kept fixed and n tends to infinity. We exhibit three different regimes for this density, depending on the tail of the degree law.

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• Exponential extinction time of the contact process on finite graphs

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