Isoperimetry and heat kernel decay on percolation clusters

• 成果类型: Article
• 署名作者: Mathieu, P; Remy, E
• 署名单位: Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 100-128
• 关键词: random-walk

摘要

We prove that the heat kernel on the infinite Bernoulli percolation cluster in Z(d) almost surely decays faster than t(-d/2). We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy.