Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks

• 成果类型: Article
• 署名作者: Erschler, Anna
• 署名单位: Universite de Lille
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-005-0495-7
• 发表日期: 2006
• 页码: 560-586
• 关键词: lamplighter group; Lower bounds; MANIFOLDS

摘要

We prove an isoperimetric inequality for wreath products of Markov chains with variable fibers. We use isoperimetric inequalities for wreath products to estimate the return probability of random walks on infinite groups and graphs, drift of random loops, the expected value E(exp(-tR(n) )), where R (n) is the number of distinct sites, visited up to the moment n, and, more generally, E[exp (-Sigma(z:Lz),(n not equal 0) F(L-z,L-n, z)) (where L-z,L-n is the number of visits of z up to the moment n and F(x, y) is some non-negative function).