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May 2008 Hitting probability of a distant point for the voter model started with a single 1
Mathieu Merle
Ann. Probab. 36(3): 807-861 (May 2008). DOI: 10.1214/009117907000000286

Abstract

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.

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Mathieu Merle. "Hitting probability of a distant point for the voter model started with a single 1." Ann. Probab. 36 (3) 807 - 861, May 2008. https://doi.org/10.1214/009117907000000286

Information

Published: May 2008
First available in Project Euclid: 9 April 2008

zbMATH: 1151.60048
MathSciNet: MR2408575
Digital Object Identifier: 10.1214/009117907000000286

Subjects:
Primary: 60G57, 60K35
Secondary: 60J80

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • May 2008
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