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

• Chen, Zhen-Qing ^[1] ; Croydon, David A. ^[2] ; Kumagai, Takashi. ^[3]
  1. [1] University of Washington

     University of Washington

     Estados Unidos

     
  2. [2] University of Warwick

     University of Warwick

     Reino Unido

     
  3. [3] Kyoto University

     Kyoto University

     Kamigyō-ku, Japón

     

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 4, 2015, págs. 1594-1642
• Idioma: inglés
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  • 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.