* K. Ravishankar (SUNY, New Paltz) - MAP5-UMR 8145

# Voter model perturbation on Z and Brownian net with killing

vendredi 14 juin 2013, 14h15 - 15h00

I will start with the description of a modification of the nearest neighbor voter model (with possibly more than 2 opinions or colors) where in addition to the voter dynamics the colors switch at random in the bulk and at the boundaries. To specify the colors at time

$t > 0 one follows the dual \left(genealogy\right) process which is coalescing random walk with branching and killing until either killing point or time zero is reached and then move up along the arrows with color information to obtain the color at time t.$

The diffusive scaling limit of the dual where the branching and killing are taken to zero at the appropriate rate is a Brownian net with killing. I will describe the construction and some of the relevant properties of this object. These results apply to Potts model and its continuum limit and are the one dimensional counterpart to recent results of Cox, Durrett and Perkins in three or more dimensions.

(The first part is joint work with C.M. Newman and Y. Moylevskky and the second part is joint work with C.M. Newman and E. Schertzer.)