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Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction
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Mathew Joseph, UNIVERSITY OF WISCONSIN MADISON
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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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Full text: PDF
Pages: 1268-1289
Published on: June 3, 2009
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Electronic Journal of Probability. ISSN: 1083-6489 |
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