CLT for NESS of a reaction-diffusion model

• 成果类型: Article
• 署名作者: Goncalves, P.; Jara, M.; Marinho, R.; Menezes, O.
• 署名单位: Universidade de Lisboa; Universidade Federal de Santa Maria (UFSM); Universidade Federal da Bahia
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01293-1
• 发表日期: 2024
• 页码: 337-377
• 关键词: large deviations; particle-systems; nonequilibrium; limit; hydrodynamics; fluctuations

摘要

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions d <= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d \le 3$$\end{document} we show a central limit theorem for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.