Author:

Keywords:

sandpile dynamics, nonlocal interactions, interacting particle systems, thermodynamic limit, self-organized criticality, Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, SELF-ORGANIZED CRITICALITY, math-ph, math.MP, math.PR, 82C22; 60K35, 0101 Pure Mathematics, 0104 Statistics, 4904 Pure mathematics, 4905 Statistics

Abstract:

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of self-organized criticality.