Annals of Applied Probability

Directional decay of the Green's function for a random nonnegative potential on ${\bf Z}\sp d$

Martin P. W. Zerner

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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.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 1 (1998), 246-280.

Dates
First available in Project Euclid: 29 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1027961043

Digital Object Identifier
doi:10.1214/aoap/1027961043

Mathematical Reviews number (MathSciNet)
MR1620370

Zentralblatt MATH identifier
0938.60098

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

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

Citation

Zerner, Martin P. W. Directional decay of the Green's function for a random nonnegative potential on ${\bf Z}\sp d$. Ann. Appl. Probab. 8 (1998), no. 1, 246--280. doi:10.1214/aoap/1027961043. https://projecteuclid.org/euclid.aoap/1027961043


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