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arXiv · 2212.12579

Abelian Sandpiles on Cylinders

Jean-Pierre Eckmann·Tatiana Nagnibeda·Aymeric Perriard
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Abstract

We study here a variant of the Abelian Sandpile Model, where the playground is a cylinder of width $w$ and of circumference c. When c << w, we describe a phenomenon which has not been observed in other geometries: the probability distribution of avalanche sizes has a ladder structure, with the first step consisting of avalanches of size up to w c/2 that are essentially equiprobable, except for a small exponential tail of order about 10c. We explain this phenomenon and describe subsequent steps.

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Jean-Pierre Eckmann, Tatiana Nagnibeda, Aymeric Perriard. 2022-12-23. Abelian Sandpiles on Cylinders. https://doi.org/10.1088/1751-8121%2Facc435

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