GAUSSIAN ESTIMATES FOR MARKOV-CHAINS AND RANDOM-WALKS ON GROUPS

• 成果类型: Article
• 署名作者: HEBISCH, W; SALOFFCOSTE, L
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); University of Wroclaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989263
• 发表日期: 1993
• 页码: 673-709
• 关键词: lie-groups; harmonic-functions; polynomial-growth; POWERS

摘要

A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular group G which is compactly generated. Moreover, if G has polynomial volume growth, the Gaussian upper bound can be complemented with a similar lower bound. Various applications are presented. In the process, we offer a new proof of Varopoulos' results relating the uniform decay of convolution powers to the volume growth of G.