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Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
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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 ISSN 0091-1798.
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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 | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) | ||||||
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 Shinkōkai [Japan Society for the Promotion of Science] (NGS) | ||||||
Grant number: | DMS-1206276 (NSF), 11128101 (NSFC), (B) 22340017 (JSPS), (A) 25247007 (JSPS) | ||||||
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