A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is assumed. The proof is based on a method developed by Sznitman (1994) for Brownian motion among Poissonian potential. In particular, the LDP holds for potentials with polynomially decaying correlations such as the classical potentials studied by L. Pastur (1977) and R. Fukushima (2008) and the potentials recently introduced by H. Lacoin (2012).
Publié le : 2019-01-15
Classification:
shape theorem,
Lyapunov exponents,
Brownian motion,
stationary random potential,
large deviations,
82B41, 60K37,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-01308838,
author = {Boivin, Daniel and L\^e, Thi Thu Hien},
title = {QUENCHED LARGE DEVIATIONS FOR BROWNIAN MOTION IN A RANDOM POTENTIAL},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01308838}
}
Boivin, Daniel; Lê, Thi Thu Hien. QUENCHED LARGE DEVIATIONS FOR BROWNIAN MOTION IN A RANDOM POTENTIAL. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-01308838/