Asymptotic behavior of edge-reinforced random walks

• 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: 10.1214/009117906000000674
• 发表日期: 2007
• 页码: 115-140
• 关键词: markov-chains

摘要

In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given by random weights on the edges. The edge weights decay exponentially in space. The process converges to a stationary process. We provide asymptotic bounds for the range of the random walker up to a given time, showing that it localizes much more than an ordinary random walker. The random environment is described in terms of an infinite-volume Gibbs measure.