RECURRENCE OF EDGE-REINFORCED RANDOM WALK ON A TWO-DIMENSIONAL GRAPH

• 成果类型: Article
• 署名作者: Merkl, Franz; Rolles, Silke W. W.
• 署名单位: University of Munich; Technical University of Munich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP446
• 发表日期: 2009
• 页码: 1679-1714
• 关键词: random environment

摘要

We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from Z(2) by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edge-reinforced random walk on these graphs is recurrent. Furthermore, we derive bounds for the probability that the edge-reinforced random walk hits the boundary of a large box before returning to its starting point.