Translator Disclaimer
2013 A local limit theorem for random walks in balanced environments
Mikko Stenlund
Author Affiliations +
Electron. Commun. Probab. 18: 1-13 (2013). DOI: 10.1214/ECP.v18-2336


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.


Download Citation

Mikko Stenlund. "A local limit theorem for random walks in balanced environments." Electron. Commun. Probab. 18 1 - 13, 2013.


Accepted: 8 March 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60360
MathSciNet: MR3037217
Digital Object Identifier: 10.1214/ECP.v18-2336

Primary: 60K37
Secondary: 35K15, 60F15, 82C41, 82D30


Back to Top