We consider Random Walk in Random Scenery , denoted $X_n$, where the random walk is symmetric on $Z^d$, with $d>4$, and the random field is made up of i.i.d random variables with a stretched exponential tail decay, with exponent $\alpha$ with $1<\alpha$. We present asymptotics for the probability, over both randomness, that $\{X_n>n^{\beta}\}$ for $1/2<\beta<1$. To obtain such asymptotics, we establish large deviations estimates for the the self-intersection local times process.
Publié le : 2005-09-27
Classification:
random scenery,
moderate deviations,
self-intersection,
local times,
random walk,
random scenery.,
60K37,60F10,60J55,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00009063,
author = {Asselah, Amine and Castell, Fabienne},
title = {Self-Intersection Times for Random Walk, and Random Walk in Random Scenery},
journal = {HAL},
volume = {2005},
number = {0},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00009063}
}
Asselah, Amine; Castell, Fabienne. Self-Intersection Times for Random Walk, and Random Walk in Random Scenery. HAL, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/hal-00009063/