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Abelian sandpiles on infinite graphs

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The Abelian sandpile model was introduced in the physics literature as a toy model of “self-organized criticality”. Originally, it is defined as a Markov chain taking place on particle configurations on a finite graph. It received a lot of attention, since several of its characteristics, for example spatial correlations, were observed to follow power laws, akin to critical systems in statistical physics. In this talk, I will give an overview of results about limits on certain infinite graphs, including the d-dimensional integer lattice. I will also consider a perturbation of the model that has exponential decay of correlations, with rate of convergence estimates as the perturbation parameter vanishes. (In large part this is based on joint works with S.R. Athreya, R. Lyons, F. Redig and E. Saada.

This talk is part of the Probability series.

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