The spectrum of the abelian sandpile model

DOI10.1090/mcom/3565zbMath1451.82035arXiv1905.07015OpenAlexW2946342114MaRDI QIDQ5131010

Robert D. Hough, Hyojeong Son

Publication date: 31 October 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07015

zbMATH Keywords

spectral gapcut-off phenomenonabelian sandpile modelrandom walk on a group

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (1)

Cut-off for sandpiles on tiling graphs

Cites Work

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• Apollonian structure in the abelian sandpile
• Tropical curves in sandpiles
• Pattern formation in growing sandpiles with multiple sources or sinks
• Sandpile group on the graph \(\mathcal D_n\) of the dihedral group
• Convergence of the abelian sandpile
• Cut-off for sandpiles on tiling graphs
• The Looping Rate and Sandpile Density of Planar Graphs
• Self-organized criticality
• Abelian sandpile model on the Husimi lattice of square plaquettes
• Self-organized critical state of sandpile automaton models
• The cutoff phenomenon in finite Markov chains.

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