Metastability for the contact process on the preferential attachment graph
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).
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 DOI:
 10.48550/arXiv.1502.05633
 arXiv:
 arXiv:1502.05633
 Bibcode:
 2015arXiv150205633H
 Keywords:

 Mathematics  Probability
 EPrint:
 45 pages