Quenched invariance principles for random walks and elliptic diffusions in random media with boundary

Zhen Qing Chen, David A. Croydon, Takashi Kumagai

研究成果: Article査読

6 被引用数 (Scopus)

抄録

Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk on a supercritical percolation cluster or among random conductances bounded uniformly from below in a half-space, quarter-space, etc., converges when rescaled diffusively to a reflecting Brownian motion, which has been one of the important open problems in this area. We establish a similar result for the random conductance model in a box, which allows us to improve existing asymptotic estimates for the relevant mixing time. Furthermore, in the uniformly elliptic case, we present quenched invariance principles for domains with more general boundaries.

本文言語English
ページ(範囲)1594-1642
ページ数49
ジャーナルAnnals of Probability
43
4
DOI
出版ステータスPublished - 2015
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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