The random conductance model with Cauchy tails

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 p_n²t^ω(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for p_n²t^ω(x, y) for all x, y in a ball.