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

First available in Project Euclid: 29 July 2002

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Zentralblatt MATH identifier

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)

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


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.

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