Metastability for the contact process on the preferential attachment graph

Van Hao Can

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arXiv · 1502.05633

Metastability for the contact process on the preferential attachment graph

Van Hao Can

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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 $\lambda$ with positive probability. More precisely, they showed that with probability $\lambda^{\Theta (1)}$, 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).

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Van Hao Can. 2015-02-19. Metastability for the contact process on the preferential attachment graph. https://arxiv.org/abs/1502.05633

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