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:
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arXiv e-prints
- Pub Date:
- February 2015
- DOI:
- 10.48550/arXiv.1502.05633
- arXiv:
- arXiv:1502.05633
- Bibcode:
- 2015arXiv150205633H
- Keywords:
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- Mathematics - Probability
- E-Print:
- 45 pages