RANDOM WALKS ON DYNAMICAL RANDOM ENVIRONMENTS WITH NONUNIFORM MIXING

• 成果类型: Article
• 署名作者: Blondel, Oriane; Hilario, Marcelo R.; Teixeira, Augusto
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1414
• 发表日期: 2020
• 页码: 2014-2051
• 关键词: large numbers; ising-model; LAW; fluctuations; front

摘要

In this paper, we study random walks on dynamical random environments in 1 + 1 dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a concentration inequality around the asymptotic speed. The mixing hypothesis imposes a polynomial decay rate of covariances on the environment with sufficiently high exponent but does not impose uniform mixing. Examples of environments for which our methods apply include the contact process and Markovian environments with a positive spectral gap, such as the East model. For the East model, we also obtain that the distinguished zero satisfies a law of large numbers with strictly positive speed.