The Library
Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
Tools
Tools
Tools
Chen, Zhen-Qing, Croydon, David A. and Kumagai, Takashi (2015) Quenched invariance principles for random walks and elliptic diffusions in random media with boundary. The Annals of Probability, 43 (4). pp. 1594-1642. doi:10.1214/14-AOP914
|
PDF
WRAP_Croydon_16120_confirm%3D18304b1a.pdf - Submitted Version - Requires a PDF viewer. Download (1017Kb) | Preview |
Official URL: http://dx.doi.org/10.1214/14-AOP914
Abstract
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 amongst 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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Dirichlet forms | ||||||
| Journal or Publication Title: | The Annals of Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 0091-1798 | ||||||
| Official Date: | 3 June 2015 | ||||||
| Dates: |
|
||||||
| Volume: | 43 | ||||||
| Number: | 4 | ||||||
| Page Range: | pp. 1594-1642 | ||||||
| DOI: | 10.1214/14-AOP914 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access | ||||||
| Funder: | National Science Foundation (U.S.) (NSF), Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), Nihon Gakujutsu ShinkÅkai [Japan Society for the Promotion of Science] (NGS) | ||||||
| Grant number: | DMS-1206276 (NSF), 11128101 (NSFC), (B) 22340017 (JSPS), (A) 25247007 (JSPS) | ||||||
| Adapted As: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
