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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Random walks with unbounded jumps among random conductances I: Uniform quenched CLT

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Author(s):
Gallesco, Christophe [1] ; Popov, Serguei
Total Authors: 2
Affiliation:
[1] Univ Campinas UNICAMP, Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: ELECTRONIC JOURNAL OF PROBABILITY; v. 17, p. 1-22, OCT 4 2012.
Web of Science Citations: 3
Abstract

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched uniform invariance principle for the random walk. This means that the rescaled trajectory of length n is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval of length O (root n) around the origin. (AU)