Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction
Mathew Joseph, UNIVERSITY OF WISCONSIN MADISON
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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