The abelian sandpile model on a random binary tree

Details The abelian sandpile model on a random binary tree The abelian sandpile model on a random binary tree

2012-02-23

arxiv.org/abs/1202.5131v2

Mathematics

Probability

30 pages, 6 figures

Scientific paper

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 (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.

Affiliated with

Also associated with

No associations

Rating

The abelian sandpile model on a random binary tree does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The abelian sandpile model on a random binary tree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The abelian sandpile model on a random binary tree will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-659497