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.
Publié le : 1996-07-14
Classification:
Brownian motion,
Poissonian potential,
random metrics,
fluctuations,
Lyapounov norms,
60K35,
82D30
@article{1065725191,
author = {Sznitman, Alain-Sol},
title = {Distance fluctuations and Lyapounov exponents},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1507-1530},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725191}
}
Sznitman, Alain-Sol. Distance fluctuations and Lyapounov exponents. Ann. Probab., Tome 24 (1996) no. 2, pp. 1507-1530. http://gdmltest.u-ga.fr/item/1065725191/