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

Xiaofeng Xue (1) , Linjie Zhao (2)

1 BJTU - Beijing Jiaotong University
2 Paradyse - Systèmes de particules et systèmes dynamiques

This paper is a further investigation of the problem studied in [Xue & Zhao, Stochastic processes and their applications, 2020], where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on Zd , 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.

Mots clés: normalized binary contact path process; non-equilibrium fluctuations; fourth moment; generalized OU process

Domaines: Probabilités [math.PR]

Xiaofeng Xue, Linjie Zhao. Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process. Stochastic Processes and their Applications, 2021. ⟨hal-03103489⟩