The Abelian sandpile model on a random binary tree

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

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2 Citaten (Scopus)

Samenvatting

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.
Originele taal-2Engels
Pagina's (van-tot)653-677
TijdschriftJournal of Statistical Physics
Volume147
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 2012

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