Speaker:  Viktor Kiss, Cornell University
Title: The Devil's staircase phenomenon for random graphs and chip-firing on graphons
Time: 2:30 PM, Monday, April 9, 2018
Place:  Malott 206

Abstract:In the parallel chip-firing game, each vertex of a graph has a certain amount of chips. One step consists of simultaneously firing all vertices with at least as many chips as their degree, where firing a vertex means making it pass a chip to each of its neighbors. The game eventually enters a period, hence it makes sense to define the activity of the game as the average number of firings per time step.

Lionel Levine showed that in some way, the activity of a chip-configuration defined on a complete graph likes to be close to rational numbers having small denominator. We show an analogue statement for Erdős-Rényi random graphs, by extending the notions of parallel chip-firing to graphons. Joint work with Lionel Levine and Lilla Tóthmérész.