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arXiv · 1807.01809

Mean-field avalanche size exponent for sandpiles on Galton-Watson trees

Antal Jarai·Wioletta M. Ruszel·Ellen Saada
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Abstract

We show that in abelian sandpiles on infinite Galton-Watson trees, the probability that the total avalanche has more than $t$ topplings decays as $t^{-1/2}$. We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (2003), that was previously used by Lyons, Morris and Schramm (2008) to study uniform spanning forests on $\mathbb{Z}^d$, $d\geq 3$, and other transient graphs.

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Antal Jarai, Wioletta M. Ruszel, Ellen Saada. 2018-07-04. Mean-field avalanche size exponent for sandpiles on Galton-Watson trees. https://arxiv.org/abs/1807.01809

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