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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The spectrum of the abelian sandpile model
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by Robert Hough and Hyojeong Son HTML | PDF
Math. Comp. 90 (2021), 441-469 Request permission


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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Additional Information
  • Robert Hough
  • Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York, 11794
  • MR Author ID: 873503
  • Email:
  • Hyojeong Son
  • Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York, 11794
  • Address at time of publication: Department of Mathematics and Statistics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899
  • ORCID: 0000-0001-5125-3364
  • Email:
  • Received by editor(s): May 20, 2019
  • Received by editor(s) in revised form: February 3, 2020, and May 13, 2020
  • Published electronically: August 26, 2020
  • Additional Notes: This material is based upon work supported by the National Science Foundation under agreements No. DMS-1712682 and DMS-1802336. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
    The second author was supported by a fellowship from the Summer Math Foundation at Stony Brook.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 441-469
  • MSC (2010): Primary 82C20, 60B15, 60J10
  • DOI:
  • MathSciNet review: 4166468