Thermodynamic Limit of the Abelian Sandpile Model on $Z^d$

A.A. Jarai

2005, v.11, №2, 313-336

ABSTRACT

We review basic properties of the Abelian sandpile model and describe recent progress made regarding its infinite volume limit on $Z^d$. In particular, we discuss the existence of the infinite volume limit of the stationary measure for $d \ge 2$, existence of infinite volume addition operators for $d \ge 3$, and construction of an infinite volume process for $d \ge 5$. We give an overview of the techniques relevant for these constructions.

Keywords: Abelian sandpile model,uniform spanning tree,thermodynamic limit,waves,two-component spanning forest

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