The contact process on the regular tree with random vertex weights

2017/03/07 by Pan, Yu, Chen, Dayue, Xue, Xiaofeng
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1703.02253

Abstract

This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection propagates through the edge connecting vertices x and y at rate λρ(x)ρ(y) for some λ>0, where \ρ(x),x∈ T^d\ are i.i.d. vertex weights. We show that when d is large enough there is a phase transition at λ_c(d)∈(0,∞) such that for λλ_c(d) the contact process survives with a positive probability. Moreover, we also show that there is another phase transition at λ_e(d) such that for λ

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