## Probability Seminar: Antal A. Jarai

- Date: 03/28/2012
- Time: 15:00

University of British Columbia

Zero dissipation limit in Abelian sandpiles

Abstract

The Abelian sandpile model on the d-dimensional integer lattice is a particle system that is critical, in the sense well-known from lattice models of statistical physics. That is, several observables follow power law distributions, at least numerically, and occasionally this can be proved. Here we study a natural one parameter family of models called dissipative sandpiles, where a small amount gamma of mass can be lost (dissipated) on each toppling. As gamma approaches 0, the critical model is recovered, while for any gamma > 0, the model has exponential decay of correlations. After discussing some basic properties, I will present estimates in d = 2 and 3, on how fast the stationary measure of the dissipative model approaches the critical sandpile measure. (Partly joint work with F. Redig and E. Saada.)