The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions d=2 or 3, we obtain the precise asymptotic behavior of this probability. We use the scaling limit of the voter model started from a single 1 at the origin in terms of super-Brownian motion under its excursion measure. This invariance principle was stated by Bramson, Cox and Le Gall, as a consequence of a theorem of Cox, Durrett and Perkins. Less precise estimates are derived in dimension d≥4.
Publié le : 2008-05-15
Classification:
Voter model,
hitting probability,
super-Brownian motion,
coalescing random walk,
60K35,
60G57,
60J80
@article{1207749082,
author = {Merle, Mathieu},
title = {Hitting probability of a distant point for the voter model started with a single 1},
journal = {Ann. Probab.},
volume = {36},
number = {1},
year = {2008},
pages = { 807-861},
language = {en},
url = {http://dml.mathdoc.fr/item/1207749082}
}
Merle, Mathieu. Hitting probability of a distant point for the voter model started with a single 1. Ann. Probab., Tome 36 (2008) no. 1, pp. 807-861. http://gdmltest.u-ga.fr/item/1207749082/