RANDOM WALK ON RANDOM WALKS: LOW DENSITIES

• 成果类型: Article
• 署名作者: Blondel, Oriane; Hilario, Marcelo R.; dos Santos, Renato S.; Sidoravicius, Vladas; Teixeira, Augusto
• 署名单位: Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); Universidade Federal de Minas Gerais; New York University; NYU Shanghai
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1537
• 发表日期: 2020
• 页码: 1614-1641
• 关键词: large numbers; symmetric exclusion; LAW; environment

摘要

We consider a random walker in a dynamic random environment given by a system of independent discrete-time simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Surprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or nonlazy random walks, which is related to a notion of permeability of the system. We also provide a strong law of large numbers, a functional central limit theorem and large deviation bounds under an ellipticity condition.