Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction

Details Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction

2008-09-01

arxiv.org/abs/0809.0320v1

Mathematics

Probability

21 pages, 2 figures

Scientific paper

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 a functional CLT 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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