Metastability for the contact process on the preferential attachment graph

van Hao Can (1)

1 I2M - Institut de Mathématiques de Marseille

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).

Mots clés: random graphs; Contact process; metastability.; preferential attachment graph

Domaines: Probabilités [math.PR]

van Hao Can. Metastability for the contact process on the preferential attachment graph. 2017. ⟨hal-01118698v3⟩