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Solvable and algebraic systems on infinite ladder

Shirai, T. & Verbitskiy, E., Dec-2016, In : Indagationes mathematicae-New series. 27, 5, p. 1162-1183 22 p.

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  • Solvable and algebraic systems on infinite ladder

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DOI

We consider two solvable models with equal entropy on the infinite ladder graph Z x {1, 2}: the uniform spanning forest (USF), the abelian sandpile (ASM). We show that the symbolic models (abelian sandpile and spanning forest) are equal entropy symbolic covers of a certain algebraic dynamical system. In the past results of this nature have been established for sandpile models on lattices Z(d). But we present a first example in case of spanning trees.
Original languageEnglish
Pages (from-to)1162-1183
Number of pages22
JournalIndagationes mathematicae-New series
Volume27
Issue number5
Publication statusPublished - Dec-2016

    Keywords

  • Uniform spanning forest, Abelian sandpiles, Algebraic dynamics, Homoclinic points, Symbolic covers, SELF-ORGANIZED CRITICALITY, GROUP AUTOMORPHISMS, SANDPILE, ENTROPY, MODELS

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