Sandpile probabilities on triangular and hexagonal lattices

TL;DR

This paper analyzes the Abelian sandpile model on triangular and hexagonal lattices, computing height probabilities and exploring the model's universality properties on different plane geometries.

Contribution

It provides explicit calculations of height probabilities for the sandpile model on these lattices and discusses their universality features.

Findings

Computed height probabilities on full and half-planes

Identified universality properties of the sandpile model

Extended understanding of sandpile behavior on non-square lattices

Abstract

We consider the Abelian sandpile model on triangular and hexagonal lattices. We compute several height probabilities on the full plane and on half-planes, and discuss some properties of the universality of the model.