SYMMETRIC EXCLUSION AS A RANDOM ENVIRONMENT: INVARIANCE PRINCIPLE

• 成果类型: Article
• 署名作者: Jara, Milton; Menezes, Otavio
• 署名单位: Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universidade de Lisboa
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1466
• 发表日期: 2020
• 页码: 3124-3149
• 关键词: additive-functionals; equilibrium fluctuations; random-walks; limit

摘要

We establish an invariance principle for a one-dimensional random walk in a dynamic random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes: a Brownian motion and a Gaussian process with stationary increments.