The spectrum of the abelian sandpile model
Probability
2021-05-25 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1905.07015,
title = {The spectrum of the abelian sandpile model},
author = {Robert Hough and Hyojeong Son},
journal= {arXiv preprint arXiv:1905.07015},
year = {2021}
}
Comments
This is the second part of the original manuscript arXiv:1902.04174, which contains numerical calculation of the spectral factors