MARKOV-CHAINS INDEXED BY TREES

• 成果类型: Article
• 署名作者: BENJAMINI, I; PERES, Y
• 署名单位: Yale University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988857
• 发表日期: 1994
• 页码: 219-243
• 关键词: random-walks; percolation; capacity

摘要

We study a variant of branching Markov chains in which the branching is governed by a fixed deterministic tree T rather than a Galton-Watson process. Sample path properties of these chains are determined by an interplay of the tree structure and the transition probabilities. For instance, there exists an infinite path in T with a bounded trajectory iff the Hausdorff dimension of T is greater than log(1/rho) where rho is the spectral radius of the transition matrix.