The survival probability of the high-dimensional contact process with random vertex weights on the oriented lattice

TL;DR

This paper investigates the asymptotic survival probability of a high-dimensional contact process with random vertex weights on an oriented lattice, revealing how the probability behaves as the dimension increases.

Contribution

It provides the first detailed asymptotic analysis of the survival probability for this process in high dimensions, using novel auxiliary models.

Findings

Survival probability approaches a specific limit as dimension grows

Branching process with random weights effectively models the process

Main result characterizes the asymptotic behavior conditioned on initial infection

Abstract

This paper is a further study of Reference \cite{Xue2015}. We are concerned with the contact process with random vertex weights on the oriented lattice. Our main result gives the asymptotic behavior of the survival probability of the process conditioned on only one vertex is infected at $t=0$ as the dimension grows to infinity. A SIR model and a branching process with random vertex weights are the main auxiliary tools for the proof of the main result.