HARMONIC MAPS ON AMENABLE GROUPS AND A DIFFUSIVE LOWER BOUND FOR RANDOM WALKS

• 成果类型: Article
• 署名作者: Lee, James R.; Peres, Yuval
• 署名单位: University of Washington; University of Washington Seattle; Microsoft
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP779
• 发表日期: 2013
• 页码: 3392-3419
• 关键词: compression

摘要

We prove diffusive lower bounds on the rate of escape of the random walk on infinite transitive graphs. Similar estimates hold for finite graphs, up to the relaxation time of the walk. Our approach uses nonconstant equivariant harmonic mappings taking values in a Hilbert space. For the special case of discrete, amenable groups, we present a more explicit proof of the Mok-Korevaar-Schoen theorem on the existence of such harmonic maps by constructing them from the heat flow on a Folner set.