MARTIN CAPACITY FOR MARKOV-CHAINS

• 成果类型: Article
• 署名作者: BENJAMINI, I; PEMANTLE, R; PERES, Y
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988187
• 发表日期: 1995
• 页码: 1332-1346
• 关键词: random-walks; percolation; trees

摘要

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda is classically estimated using the capacity of Lambda with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices and also to explain a connection found by Lyons between capacity and percolation on trees.