We derive a large deviation principle for the position at large
times $t$ of a one-dimensional annealed Brownian motion in a Poissonian
potential in the critical spatial scale $t^{1/3}$. Here
“annealed” means that averages are taken with respect to both the
path and environment measures. In contrast to the $d$-dimensional case for $d
\geq 2$ in the critical scale $t^{d/(d+2)}$ as treated by Sznitman, the rate
function which measures the large deviations exhibits three different regimes.
These regimes depend on the position of the path at time $t$. Our large
deviation principle has a natural application to the study of a one-dimensional
annealed Brownian motion with a constant drift in a Poissonian potential.
Publié le : 1997-10-14
Classification:
Large deviations,
Poisson potential,
Brownian motion with drift,
60F10,
82D30
@article{1023481109,
author = {Povel, Tobias},
title = {Critical large deviations of one-dimensional annealed Brownian
motion in a Poissonian potential},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1735-1773},
language = {en},
url = {http://dml.mathdoc.fr/item/1023481109}
}
Povel, Tobias. Critical large deviations of one-dimensional annealed Brownian
motion in a Poissonian potential. Ann. Probab., Tome 25 (1997) no. 4, pp. 1735-1773. http://gdmltest.u-ga.fr/item/1023481109/