SCALING LIMITS OF RANDOM WALKS, HARMONIC PROFILES, AND STATIONARY NONEQUILIBRIUM STATES IN LIPSCHITZ DOMAINS

• 成果类型: Article
• 署名作者: Dello Schiavo, Lorenzo; Portinale, Lorenzo; Sau, Federico
• 署名单位: Institute of Science & Technology - Austria; University of Bonn; University of Catania
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2007
• 发表日期: 2024
• 页码: 1789-1845
• 关键词: dirichlet problem; exclusion process; CONVERGENCE; REGULARITY; laplacian; robin; INEQUALITY; TRANSITION; EQUATIONS; Operators

摘要

We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Omega, with both fast and slow boundary. For the random walks on Omega dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Omega with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously derive the hydrodynamic and hydrostatic limits for SEP/SIP on Omega, and analyze their stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems.