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July 1996 Distance fluctuations and Lyapounov exponents
Alain-Sol Sznitman
Ann. Probab. 24(3): 1507-1530 (July 1996). DOI: 10.1214/aop/1065725191

Abstract

We associate certain translation invariant random metrics on $\mathbb{R}^d$ to Brownian motion evolving in a truncated Poissonian potential. These metrics behave over large distances, in an appropriate sense, like certain deterministic norms (the so-called Lyapounov exponents). We prove here upper bounds on the size of fluctuations of the metrics around their mean. Under an additional assumption of rotational invariance, we also derive upper bounds on the difference between the mean of the metrics and the Lyapounov norms.

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Alain-Sol Sznitman. "Distance fluctuations and Lyapounov exponents." Ann. Probab. 24 (3) 1507 - 1530, July 1996. https://doi.org/10.1214/aop/1065725191

Information

Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0871.60088
MathSciNet: MR1411504
Digital Object Identifier: 10.1214/aop/1065725191

Subjects:
Primary: 60K35, 82D30

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 3 • July 1996
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