Probability Seminar: Antal A. Jarai

  • Date: 03/28/2012
  • Time: 15:00
Antal A. Jarai

University of British Columbia


Zero dissipation limit in Abelian sandpiles



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.)

Other Information: 

Location: WMAX 110


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