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arXiv · 2004.13104

The devil's staircase for chip-firing on random graphs and on graphons

Viktor Kiss·Lionel Levine·Lilla Tóthmérész
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Abstract

We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erd\H{o}s--R\'enyi random graph. We show that in various situations the resulting activity diagrams converge to a devil's staircase as we increase the number of vertices. Our method is to generalize the parallel chip-firing to graphons, and to prove a continuity result for the activity. We also show that the activity of a chip configuration on a graphon does not necessarily exist, but it does exist for every chip configuration on a large class of graphons.

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BibTeXRIS

Viktor Kiss, Lionel Levine, Lilla Tóthmérész. 2020-04-27. The devil's staircase for chip-firing on random graphs and on graphons. https://doi.org/10.1002/rsa.21255

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