Probability of hitting a far point for the voter model

  • Start Date: 09/27/2006
  • End Date: 09/28/2006

Mathieu Merle (U. British Columbia)


University of British Columbia


We consider a voter model on the integer lattice started with a single
one at the origin. In dimensions 2 and 3, we establish the precise
asymptotic behaviour of the probability for the voter model to hit a
distant point. We use the scaling limit of the voter model started from
a single one in terms of super-Brownian motion under its excursion
measure. This invariant principle was proved by Bramson Cox and Le
Gall, as a consequence of a theorem of Cox, Durrett and Perkins. We
also derive less precise estimates in dimension less than 4.

Other Information: 

Probability Seminar 2006