RANDOM DIRICHLET ENVIRONMENT VIEWED FROM THE PARTICLE IN DIMENSION d ≥ 3

• 成果类型: Article
• 署名作者: Sabot, Christophe
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP699
• 发表日期: 2013
• 页码: 722-743
• 关键词: quenched invariance-principles; transient random-walks; central-limit-theorem; large numbers; LAW

摘要

We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z(d), RWDE are parameterized by a 2d-tuple of positive reals called weights. In this paper, we characterize for d >= 3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result and from [Ann. Inst. Henri Poincare Probab. Stat. 47 (2011) 1-8] a complete description of the ballistic regime for d >= 3.