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

Christophe Gallesco (University of Campinas - UNICAMP)
Serguei Popov (University of Campinas - UNICAMP)


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 $O(\sqrt{n})$ around the origin.

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Pages: 1-22

Publication Date: October 4, 2012

DOI: 10.1214/EJP.v17-1826


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