Leírás
Előadó: Kiss Viktor
Cím: The devil’s staircase for chip-firing on random graphs and on graphons
Absztrakt: The parallel chip-firing game is a dynamical system which was first explored by physicists. A graph is given, with a certain amount of chips on each vertex. In a step, all vertices having at least as many chips as their degree simultaneously topple, sending a chip through each edge incident to them. The game eventually enters a period, hence it makes sense to define the activity of the game as the average ratio of toppled vertices per time step.
Motivated by numerical experiments in which the period of the game was small with large probability, Lionel Levine showed that in some sense, the activity of a chip-configuration defined on a complete graph likes to be close to rational numbers having small denominators. We prove an analogous statement for Erdős-Rényi random graphs, by extending the notions of parallel chip-firing to graphons. Joint work with Lionel Levine and Lilla Tóthmérész.