The contact process on random hyperbolic graphs: metastability and\n critical exponents

2020/07/20 by Amitai Linker, Dieter Mitsche, Linker, Amitai +5 · 2 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Complex Network Analysis Techniques #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2007.10017

Abstract

We consider the contact process on the model of hyperbolic random graph, in\nthe regime when the degree distribution obeys a power law with exponent \χ\n\∈(1,2) (so that the degree distribution has finite mean and infinite second\nmoment). We show that the probability of non-extinction as the rate of\ninfection goes to zero decays as a power law with an exponent that only depends\non \χ and which is the same as in the configuration model, suggesting some\nuniversality of this critical exponent. We also consider finite versions of the\nhyperbolic graph and prove metastability results, as the size of the graph goes\nto infinity.\n

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