We identify the limit of the internal DLA cluster generated by Sinai's walk as the law of a functional of a Brownian motion which turns out to be a new interpretation of the Arcsine law.
Publié le : 2010-11-01
Classification:
excursion theory,
Sinai's walk,
internal DLA,
random walks in random environments,
excursion theory.,
60K37, 60F05,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00371608,
author = {Enriquez, Nathana\"el and Lucas, Cyrille and Simenhaus, Fran\c cois},
title = {The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk},
journal = {HAL},
volume = {2010},
number = {0},
year = {2010},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00371608}
}
Enriquez, Nathanaël; Lucas, Cyrille; Simenhaus, François. The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk. HAL, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/hal-00371608/