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2009 Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction
Mathew Joseph
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Electron. J. Probab. 14: 1268-1289 (2009). DOI: 10.1214/EJP.v14-655

Abstract

We consider an i.i.d. random environment with a strong form of transience on the two dimensional integer lattice. Namely, the walk always moves forward in the y-direction. We prove an invariance principle for the quenched expected position of the random walk indexed by its level crossing times. We begin with a variation of the Martingale Central Limit Theorem. The main part of the paper checks the conditions of the theorem for our problem.

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Mathew Joseph. "Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction." Electron. J. Probab. 14 1268 - 1289, 2009. https://doi.org/10.1214/EJP.v14-655

Information

Accepted: 3 June 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1195.60130
MathSciNet: MR2511284
Digital Object Identifier: 10.1214/EJP.v14-655

Subjects:
Primary: 60K37
Secondary: 60F05 , 60F17 , 82D30

Keywords: central limit theorem , Green function , invariance principle , Random walk in random environment

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Vol.14 • 2009
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