@article{ECP2336,
author = {Mikko Stenlund},
title = {A local limit theorem for random walks in balanced environments},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {18},
year = {2013},
keywords = {Balanced random environment, local limit theorem, Nash inequality},
abstract = {Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems - yielding a Gaussian density multiplied by a highly oscillatory modulating factor - for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uniformly elliptic ballistic walks are now well understood. We complete the picture by proving a similar result for the only recurrent case, namely the balanced one, in which such a walk is diffusive. The method of proof is, out of necessity, entirely different from the ballistic case.},
pages = {no. 19, 1-13},
issn = {1083-589X},
doi = {10.1214/ECP.v18-2336},
url = {http://ecp.ejpecp.org/article/view/2336}}