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arXiv · 1412.1161

Contact processes with random vertex weights on oriented lattices

Xiaofeng Xue
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Abstract

In this paper we are concerned with contact processes with random vertex weights on oriented lattices. In our model, we assume that each vertex x of Z^d takes i. i. d. positive random value ρ(x). Vertex y infects vertex x at rate proportional to ρ(x)ρ(y) when and only when there is an oriented edge from y to x. We give the definition of the critical value λ_c of infection rate under the annealed measure and show that λ_c=[1+o(1)]/(dEρ^2) as d grows to infinity. Classic contact processes on oriented lattices and contact processes on clusters of oriented site percolation are two special cases of our model.

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Xiaofeng Xue. 2014-12-03. Contact processes with random vertex weights on oriented lattices. https://arxiv.org/abs/1412.1161

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