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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

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.

Citation

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Mikko Stenlund. "A local limit theorem for random walks in balanced environments." Electron. Commun. Probab. 18 1 - 13, 2013. https://doi.org/10.1214/ECP.v18-2336

Information

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

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

JOURNAL ARTICLE
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