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February 1998 Directional decay of the Green's function for a random nonnegative potential on ${\bf Z}\sp d$
Martin P. W. Zerner
Ann. Appl. Probab. 8(1): 246-280 (February 1998). DOI: 10.1214/aoap/1027961043

Abstract

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.

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Martin P. W. Zerner. "Directional decay of the Green's function for a random nonnegative potential on ${\bf Z}\sp d$." Ann. Appl. Probab. 8 (1) 246 - 280, February 1998. https://doi.org/10.1214/aoap/1027961043

Information

Published: February 1998
First available in Project Euclid: 29 July 2002

zbMATH: 0938.60098
MathSciNet: MR1620370
Digital Object Identifier: 10.1214/aoap/1027961043

Subjects:
Primary: 60K35 , 82D30

Keywords: asymptotic shape , first passage percolation , Green's function , large deviations , Lyapounov exponent , Random potential , Random walk

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 1 • February 1998
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