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...

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Bibliographic Details
Published in:Stochastic processes and their applications 2012, Vol.122 (1), p.277-304
Main Authors: Kosygina, Elena, Mountford, Thomas
Format: Article
Language:English
Subjects:
Annealed measure
Ballisticity
Lyapunov exponents
Random potential
Random walk
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2011.08.008