The Abelian Sandpile Model on a Random Binary Tree

F. Redig, W.M. Ruszel, E. Saada

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

We study the abelian sandpile model on a random binary tree. Using a transfer
matrix approach introduced by Dhar and Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process survives with positive probability) exponential decay of avalanche sizes. This shows a phase transition phenomenon between exponential decay and power law decay of avalanche sizes. Our main technical tools are: (1) A recursion for the ratio between the numbers of weakly and strongly allowed configurations which is proved to have a well-defined stochastic solution; (2) quenched and annealed estimates of the eigenvalues of a product of n random transfer
matrices.

Original languageEnglish
Pages (from-to)653-677
Number of pages25
JournalJournal of Statistical Physics
Volume147
Issue number4
DOIs
Publication statusPublished - 2012

Keywords

  • Sandpile models
  • Random binary trees
  • Phase transition

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