THE SPECTRUM OF THE ABELIAN SANDPILE MODEL

Robert Hough; Hyojeong Son

doi:10.1090/mcom/3565

THE SPECTRUM OF THE ABELIAN SANDPILE MODEL

Robert Hough
, Hyojeong Son

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 parameters which govern the asymptotic spectral gap and asymptotic mixing time. This paper gives a general method of determining the spectral parameters either computationally or asymptotically, and determines the spectral parameters in specific examples.

Original language	English
Pages (from-to)	441-469
Number of pages	29
Journal	Mathematics of Computation
Volume	90
Issue number	327
DOIs	https://doi.org/10.1090/mcom/3565
State	Published - Jan 2021

Keywords

Abelian sandpile model
cut-off phenomenon.
random walk on a group
spectral gap

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10.1090/mcom/3565

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title = "THE SPECTRUM OF THE ABELIAN SANDPILE MODEL",

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 parameters which govern the asymptotic spectral gap and asymptotic mixing time. This paper gives a general method of determining the spectral parameters either computationally or asymptotically, and determines the spectral parameters in specific examples.",

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AU - Son, Hyojeong

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AB - 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 parameters which govern the asymptotic spectral gap and asymptotic mixing time. This paper gives a general method of determining the spectral parameters either computationally or asymptotically, and determines the spectral parameters in specific examples.

KW - Abelian sandpile model

KW - cut-off phenomenon.

KW - random walk on a group

KW - spectral gap

UR - https://www.scopus.com/pages/publications/85100207329

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DO - 10.1090/mcom/3565

M3 - Article

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SP - 441

EP - 469

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 327

ER -

THE SPECTRUM OF THE ABELIAN SANDPILE MODEL

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Keywords

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