The abelian sandpile model on a random binary tree

Abstract : We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region 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.
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Contributor : Ellen Saada <>
Submitted on : Monday, April 9, 2012 - 7:00:36 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM

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Frank Redig, Wioletta Ruszel, Ellen Saada. The abelian sandpile model on a random binary tree. Journal of Statistical Physics, Springer Verlag, 2012, 147 (4), pp.653-677. ⟨10.1007/s10955-012-0498-6⟩. ⟨hal-00686288⟩

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