Central limit theorems of occupation times of high-dimensional normalized binary contact path processes

2022/09/09 by Xiaofeng Xue, Xue, Xiaofeng
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.04182

openalex publication_date 2022/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The binary contact path process (BCPP) introduced in Griffeath (1983) describes the spread of an epidemic on a graph and is an auxiliary model in the study of improving upper bounds of the critical value of the contact process. In this paper, we are concerned with the central limit theorem of the occupation time of a normalized version of the BCPP (NBCPP) on a lattice. We show that the centred occupation time process of the NBCPP converges in finite dimensional distributions to a Brownian motion when the dimension of the lattice and the infection rate of the model are sufficiently large and the initial state of the NBCPP is distributed with a particular invariant distribution.

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