# The spectrum of the abelian sandpile model

## TL;DR

This paper introduces a general method to determine the spectral factor of the abelian sandpile model, enabling analysis of spectral gap and mixing time on various graph structures, with specific example applications.

## Contribution

It provides a new computational and asymptotic approach to find the spectral factor of the abelian sandpile model on different graphs.

## Key findings

- Method for determining spectral factor computationally and asymptotically
- Application to specific graph examples
- Insights into spectral gap and mixing time behavior

## Abstract

In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary conditions, and identified spectral factors which govern the asymptotic spectral gap and asymptotic mixing time. This article gives a general method of determining the spectral factor either computationally or asymptotically and performs the determination in specific examples.