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arXiv · 1103.0515

Crossing velocities for an annealed random walk in a random potential

Elena Kosygina·Thomas Mountford
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Abstract

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 one we show the existence of the asymptotic positive speed.

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Elena Kosygina, Thomas Mountford. 2011-08-05. Crossing velocities for an annealed random walk in a random potential. https://doi.org/10.1016/j.spa.2011.08.008

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