Probability of hitting a distant point for the voter model started with a single one

Mathieu Merle

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Probability of hitting a distant point for the voter model started with a single one

Mathieu Merle

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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 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 dimensions greater than 4.

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Mathieu Merle. 2006-09-28. Probability of hitting a distant point for the voter model started with a single one. https://arxiv.org/abs/math/0609826

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