The random conductance model with Cauchy tails

Details The random conductance model with Cauchy tails The random conductance model with Cauchy tails

2009-08-20

arxiv.org/abs/0908.2844v3

Annals of Applied Probability 2010, Vol. 20, No. 3, 869-889

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP638 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP638

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 $p^{\omega}_{n^2t}(0,y)$ in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for $p^{\omega}_{n^2t}(x,y)$ for all $x,y$ in a ball.

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