Mean field limit for survival probability of the high-dimensional contact process

Xiaofeng Xue

Statistics & Probability Letters, 2017, vol. 127, issue C, 178-184

Abstract: In this paper we are concerned with the contact process on the hypercube lattice Zd. The contact process intuitively describes the spread of the infectious disease on a graph, where an infectious vertex becomes healthy at a constant rate while a healthy vertex is infected at rate proportional to the number of infectious neighbors. As the dimension of the lattice grows to infinity, we give a mean field limit for the survival probability of the process conditioned on the event that only the origin of the lattice is infected at t=0. The binary contact path process is a main auxiliary tool for our proof.

Keywords: Contact process; Survival probability; Mean field limit (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2017.04.010

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