Probability Seminar: Antal A. Jarai
Topic
Zero dissipation limit in Abelian sandpiles
Speakers
Details
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.)
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.)
