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

2008/09/01 by Mathew Joseph, Joseph, Mathew
Mathematics · #60F05 #60F17 #60K37 #82D30 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F05 #msc:60F17 #msc:60K37 #msc:82D30

paper · pdf · doi:10.48550/arxiv.0809.0320

21 pages, 2 figures

arxiv created 2008/09/01 · arxiv updated 2009/12/01

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 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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