Transient random walks in random environment on a Galton-Watson tree

• 成果类型: Article
• 署名作者: Aidekon, Elie
• 署名单位: Sorbonne Universite; Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0114-x
• 发表日期: 2008
• 页码: 525-559
• 关键词: regular tree

摘要

We consider a transient random walk (X-n) in random environment on a Galton-Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that X-n is of order of magnitude n(Lambda), with Lambda is an element of (0, 1). We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, which improves a recent result of Collevecchio (Probab Theory Related 136(1):81-101, 2006).