ON THE TRANSIENT (T) CONDITION FOR RANDOM WALK IN MIXING ENVIRONMENT

• 成果类型: Article
• 署名作者: Guerra Aguilar, Enrique
• 署名单位: Pontificia Universidad Catolica de Chile
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1330
• 发表日期: 2019
• 页码: 3003-3054
• 关键词: large numbers; LAW

摘要

We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition (T) of Sznitman (cf. Ann. Probab. 29 (2001) 724-765). This weakens for the first time Kalikow's ballisticity assumption on mixing environments and proves the existence of arbitrary finite order moments for the approximate regeneration time of F. Comets and O. Zeitouni (Israel J. Math. 148 (2005) 87-113). The main technical tool in the proof is the introduction of renormalization schemes, which had only been considered for i.i.d. environments.