## The Annals of Probability

### Distance fluctuations and Lyapounov exponents

Alain-Sol Sznitman

#### 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.

#### Article information

Source
Ann. Probab., Volume 24, Number 3 (1996), 1507-1530.

Dates
First available in Project Euclid: 9 October 2003

https://projecteuclid.org/euclid.aop/1065725191

Digital Object Identifier
doi:10.1214/aop/1065725191

Mathematical Reviews number (MathSciNet)
MR1411504

Zentralblatt MATH identifier
0871.60088

#### Citation

Sznitman, Alain-Sol. Distance fluctuations and Lyapounov exponents. Ann. Probab. 24 (1996), no. 3, 1507--1530. doi:10.1214/aop/1065725191. https://projecteuclid.org/euclid.aop/1065725191