Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process

2020/08/24 by Xue, Xiaofeng, Zhao, Linjie
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2008.10350

Abstract

This paper is a further investigation of the problem studied in \citexue2020hydrodynamics, where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on ℤ^d, d ≥ 3, and then conjectured that a central limit theorem should hold under a non-equilibrium initial condition. We prove that the aforesaid conjecture is true when the dimension d of the underlying lattice and the infection rate λ of the process are sufficiently large.

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• Hydrodynamics of the Binary Contact Path Process
• The critical infection rate of the high-dimensional two-stage contact process
• Central limit theorems of occupation times of high-dimensional normalized binary contact path processes
• Central Limit Theorem for a Class of Linear Systems
• Non-equilibrium Fluctuations of Interacting Particle Systems