DIMENSION-FREE LOCAL CONVERGENCE AND PERTURBATIONS FOR REFLECTED BROWNIAN MOTIONS

• 成果类型: Article
• 署名作者: Banerjee, Sayan; Brown, Brendan
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1818
• 发表日期: 2023
• 页码: 376-416
• 关键词: infinite systems; rates; equilibrium; particles; stationarity; propagation; DIFFUSIONS; chaos

摘要

We describe and analyze a class of positive recurrent reflected Brownian motions (RBMs) in Rd+ for which local statistics converge to equilibrium at a rate independent of the dimension d. Under suitable assumptions on the reflection matrix, drift and diffusivity coefficients, dimension-independent stretched exponential convergence rates are obtained by estimating contrac-tions in an underlying weighted distance between synchronously coupled RBMs. We also study the symmetric Atlas model as a first step in obtaining dimension-independent convergence rates for RBMs not satisfying the above assumptions. By analyzing a pathwise derivative process and connecting it to a random walk in a random environment, we obtain polynomial conver-gence rates for the gap process of the symmetric Atlas model started from appropriate perturbations of stationarity.