Directional decay of the Green's function for a random nonnegative potential on Z\spd

Authors
Zerner, Martin P. W.
Citation
W. Zerner, Martin P., Directional decay of the Green's function for a random nonnegative potential on Z\spd, Annals of applied probability , 8(1), 1998, pp. 246-280
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
8
Issue
1
Year of publication
1998
Pages
246 - 280
Database
ACNP
SICI code
Abstract
We derive a shape theorem type result for the almost sure exponential decay of the Green's function of ..+V, where the potentials V(x),x.Zd are i.i.d. nonnegative random variables. This result implies a large deviation principle governing the position of a d-dimensional random walk moving in the same potential.