# zbMATH — the first resource for mathematics

Metastable densities for the contact process on power law random graphs. (English) Zbl 1281.82018
Summary: We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of S. Chatterjee and R. Durrett [Ann. Probab. 37, No. 6, 2332–2356 (2009; Zbl 1205.60168)], who showed that for arbitrarily small infection parameter $$\lambda$$, the survival time of the process is larger than a stretched exponential function of the number of vertices, $$n$$. We obtain sharp bounds for the typical density of infected sites in the graph, as $$\lambda$$ is kept fixed and $$n$$ tends to infinity. We exhibit three different regimes for this density, depending on the tail of the degree law.

##### MSC:
 82C22 Interacting particle systems in time-dependent statistical mechanics 05C80 Random graphs (graph-theoretic aspects) 60K35 Interacting random processes; statistical mechanics type models; percolation theory
##### Keywords:
contact process; random graphs
Full Text: