article · Journal of Statistical Physics · 2012

The Abelian Sandpile Model on a Random Binary Tree

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

Cited by 3Open access

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.

Cite this paper

APA 7

Redig, F., Ruszel, W. M., & Saada, E. (2012). The Abelian Sandpile Model on a Random Binary Tree. Journal of Statistical Physics, 147(4), 653–677. https://doi.org/10.1007/s10955-012-0498-6

MLA 9

Redig, F., et al. “The Abelian Sandpile Model on a Random Binary Tree.” Journal of Statistical Physics, vol. 147, no. 4, 2012, pp. 653–77, https://doi.org/10.1007/s10955-012-0498-6.

Chicago

Redig, F., W. M. Ruszel, and E. Saada. 2012. “The Abelian Sandpile Model on a Random Binary Tree.” Journal of Statistical Physics 147 (4): 653–77. https://doi.org/10.1007/s10955-012-0498-6.

Harvard

Redig, F., Ruszel, W.M. and Saada, E. (2012) ‘The Abelian Sandpile Model on a Random Binary Tree’, Journal of Statistical Physics, 147(4), pp. 653–677. Available at: https://doi.org/10.1007/s10955-012-0498-6.

BibTeX

@article{redig2012abelian,
  title = {{The Abelian Sandpile Model on a Random Binary Tree}},
  author = {Redig, F. and Ruszel, W. M. and Saada, E.},
  journal = {Journal of Statistical Physics},
  volume = {147},
  number = {4},
  pages = {653--677},
  year = {2012},
  doi = {10.1007/s10955-012-0498-6}
}

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