## Probability of hitting a far point for the voter model

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

Speaker(s):

Mathieu Merle (U. British Columbia)

Location:

University of British Columbia

Topic:

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