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 $O(\sqrt{n})$ around the origin.
Citation
Christophe Gallesco. Serguei Popov. "Random walks with unbounded jumps among random conductances I: Uniform quenched CLT." Electron. J. Probab. 17 1 - 22, 2012. https://doi.org/10.1214/EJP.v17-1826
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