FLUCTUATIONS AND CORRELATIONS IN WEAKLY ASYMMETRIC SIMPLE EXCLUSION ON A RING SUBJECT TO AN ATYPICAL CURRENT

• 成果类型: Article
• 署名作者: Dagallier, Benoit
• 署名单位: New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1729
• 发表日期: 2025
• 页码: 1079-1137
• 关键词: long-range correlations; large deviations; equilibrium

摘要

We consider the weakly asymmetric simple exclusion process on a ring, driven out of equilibrium by tilting the dynamics so as to enforce a macroscopic current of particles on a large time interval. In this current-biased dynamics, the tilt by the current makes the dynamics nonlocal, nonhomogeneous and induces long-range correlations. We compute the correlation structure in the large time, large size limit for a certain range of asymmetry and current strength, recovering heuristic results of Bodineau et al. (J. Stat. Phys. 133 (2008) 1013-1031). In addition, in this range of parameters, we characterise the full dynamics of fluctuations around the optimal density profile in the current-biased dynamics. The key ingredient at the microscopic scale is a precise relative entropy estimate at the level of correlations. We also discuss how to remove the (technical) restriction on the range of parameters.