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May 2021 The contact process on random hyperbolic graphs: Metastability and critical exponents
Amitai Linker, Dieter Mitsche, Bruno Schapira, Daniel Valesin
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Ann. Probab. 49(3): 1480-1514 (May 2021). DOI: 10.1214/20-AOP1489

Abstract

We consider the contact process on the model of hyperbolic random graph, in the regime when the degree distribution obeys a power law with exponent χ(1,2) (so that the degree distribution has finite mean and infinite second moment). We show that the probability of nonextinction as the rate of infection goes to zero decays as a power law with an exponent that only depends on χ and which is the same as in the configuration model, suggesting some universality of this critical exponent. We also consider finite versions of the hyperbolic graph and prove metastability results, as the size of the graph goes to infinity.

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Amitai Linker. Dieter Mitsche. Bruno Schapira. Daniel Valesin. "The contact process on random hyperbolic graphs: Metastability and critical exponents." Ann. Probab. 49 (3) 1480 - 1514, May 2021. https://doi.org/10.1214/20-AOP1489

Information

Received: 1 July 2020; Published: May 2021
First available in Project Euclid: 7 April 2021

Digital Object Identifier: 10.1214/20-AOP1489

Subjects:
Primary: 82C22
Secondary: 05C80

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • May 2021
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