Crossing velocities for an annealed random walk in a random potential

We consider a random walk in an i.i.d. non-negative potential on the d-dimensional integer lattice. The walk starts at the origin and is conditioned to hit a remote location y on the lattice. We prove that the expected time under the annealed path measure needed by the random walk to reach y grows only linearly in the distance from y to the origin. In dimension 1 we show the existence of the asymptotic positive speed. (C) 2011 Elsevier B.V. All rights reserved.


Published in:
Stochastic Processes And Their Applications, 122, 277-304
Year:
2012
Keywords:
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 Record created 2012-02-23, last modified 2018-09-13


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