In this article, we prove a large deviation principle
for the empirical drift of a one-dimensional Brownian motion with
self-repellence called the Edwards model. Our results extend
earlier work in which a law of large numbers and a
central limit theorem were derived. In the Edwards model, a path of
length T receives a penalty $e^{-\beta H_T}$, where $ H_T$ is
the self-intersection local time of the path and
$\beta\in(0,\infty)$ is a parameter called the strength of
self-repellence. We identify the rate function in the large
deviation principle for the endpoint of the path as
$\beta^{2/3} I(\beta^{-1/3}\cdot)$, with $I(\cdot)$ given in terms of
the principal eigenvalues of a one-parameter family of
Sturm--Liouville operators. We show that there exist numbers
$0
Publié le : 2003-10-14
Classification:
Self-repellent Brownian motion,
intersection local time,
Ray--Knight theorems,
large deviations,
Airy function,
60F05,
60F10,
60J55,
82D60
@article{1068646376,
author = {van der Hofstad, Remco and den Hollander, Frank and K\"onig, Wolfgang},
title = {Large deviations for the one-dimensional Edwards model},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 2003-2039},
language = {en},
url = {http://dml.mathdoc.fr/item/1068646376}
}
van der Hofstad, Remco; den Hollander, Frank; König, Wolfgang. Large deviations for the one-dimensional Edwards model. Ann. Probab., Tome 31 (2003) no. 1, pp. 2003-2039. http://gdmltest.u-ga.fr/item/1068646376/