Sandpiles on the heptagonal tiling

TL;DR

This paper investigates the behavior of sandpile models on the hyperbolic plane's heptagonal tiling, providing explicit descriptions of how these systems relax from maximal stable states.

Contribution

It offers a novel analysis of sandpile dynamics on hyperbolic tilings, extending understanding beyond Euclidean cases.

Findings

Explicit relaxation descriptions for sandpiles on heptagonal tiling

Insights into stability and perturbation effects in hyperbolic geometries

Extension of sandpile theory to non-Euclidean surfaces

Abstract

We study perturbations of the maximal stable state in a sandpile model on the set of faces of the heptagonal tiling on the hyperbolic plane. An explicit description for relaxations of such states is given.