We derive a shape theorem type result for the almost sure
exponential decay of the Green's function of $-\Delta + V$, where the
potentials $V(x), x \epsilon \mathbb{Z}^d$ 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.
Publié le : 1998-02-14
Classification:
Random walk,
random
potential,
Green's function,
asymptotic
shape,
first passage percolation,
Lyapounov
exponent,
large deviations,
60K35,
82D30
@article{1027961043,
author = {Zerner, Martin P. W.},
title = {Directional decay of the Green's function for a random nonnegative
potential on ${\bf Z}\sp d$},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 246-280},
language = {en},
url = {http://dml.mathdoc.fr/item/1027961043}
}
Zerner, Martin P. W. Directional decay of the Green's function for a random nonnegative
potential on ${\bf Z}\sp d$. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 246-280. http://gdmltest.u-ga.fr/item/1027961043/