Work

Metastability for the contact process on the preferential attachment graph

Year: 2015

Type: preprint

Abstract: We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an arbitrarily small infection rate $λ$ with positive probability. More precisely, they showed that with probability $λ^{Θ(1)}$, it survives for a time exponential in the largest degree. Here we obtain sharp bounds for the density of infected sites at a time close to exponential in the number of vertices (up to some logarithmic factor).

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.1502.05633

Author: Can, Van Hao

Institutions: Institut de Mécanique et d'Ingénierie de Bordeaux, Institut de Mathématiques de Marseille

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4301114555

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