Isoperimetric inequalities and mixing time for a random walk on a random point process

• 成果类型: Article
• 署名作者: Caputo, Pietro; Faggionato, Alessandra
• 署名单位: Roma Tre University; Sapienza University Rome
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP442
• 发表日期: 2007
• 页码: 1707-1744
• 关键词: invariance-principle; percolation; phase

摘要

We consider the random walk on a simple point process on R-d, d >= 2, whose jump rates decay exponentially in the alpha-power of jump length. The case alpha = 1 corresponds to the phonon-induced variable-range hopping in disordered solids in the regime of strong Anderson localization. Under mild assumptions on the point process, we show, for a epsilon (0, d), that the random walk confined to a cubic box of side L has a.s. Cheeger constant of order at least L-1 and mixing time of order L-2. For the Poisson point process, we prove that at a = d, there is a transition from diffusive to subdiffusive behavior of the mixing time.