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- W3022433224 abstract "We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erdős--Renyi 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." @default.
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- W3022433224 date "2020-04-27" @default.
- W3022433224 modified "2023-09-27" @default.
- W3022433224 title "The devil's staircase for chip-firing on random graphs and on graphons" @default.
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