Abstract
We consider a random walk in an i.i.d. Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a key step in the arguments, we improve the local limit theorem for pn2tω(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for pn2tω(x, y) for all x, y in a ball.
Citation
Martin T. Barlow. Xinghua Zheng. "The random conductance model with Cauchy tails." Ann. Appl. Probab. 20 (3) 869 - 889, June 2010. https://doi.org/10.1214/09-AAP638
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