Solvable and algebraic systems on infinite ladder

Tomoyuki Shirai*, Evgeny Verbitskiy

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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
DOIs
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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