Exponential extinction time of the contact process on finite graphs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Mountford, Thomas¹  Mourrat, Jean-Christophe¹  Valesin, Daniel²  Yao, Qiang³ 

[1] Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] E China Normal Univ, Sch Finance & Stat, Shanghai 200241, Peoples R China

关键词: Contact process;    Interacting particle systems;    Metastability;   

DOI  :  10.1016/j.spa.2016.01.001

来源: Elsevier

【 摘 要 】

We study the extinction time tau of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degree bounded by a given number, the expectation of tau grows exponentially with the number of vertices. Additionally, for any increasing sequence of trees of bounded degree, t divided by its expectation converges in distribution to the unitary exponential distribution. These results also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree, and provide the basis for powerful coarse-graining arguments. To demonstrate this, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett (2009), we show that, for any non-zero infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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