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.
"The Abelian sandpile model on an infinite tree." Ann. Probab. 30 (4) 2081 - 2107, October 2002. https://doi.org/10.1214/aop/1039548382