The random conductance model with Cauchy tails

Martin T. Barlow, Xinghua Zheng
2010 The Annals of Applied Probability  
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.
doi:10.1214/09-aap638 fatcat:vq2p3gp74zaofm2nywk2auxwaq