Thermodynamic Limit of the Abelian Sandpile Model on $Z^d$
2005, v.11, №2, 313-336
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