Presentation on Zoom

Graphon has recently been introduced by Lovasz, Sos, etc. to study very large graphs. A graphon can be understood as either the limit object of a convergent sequence of graphs, or, a statistical model from which to sample large random graphs. We take here the latter point of view and address the following problem: What is the probability that a random graph sampled from a graphon has a Hamiltonian decomposition? We have recently observed the following phenomenon: In the asymptotic regime where the size of the random graph goes to infinity, the probability tends to be either 0 or 1, depending on the underlying graphon. In this talk, we establish this “zero-one” property for the class of step-graphons and provide a geometric characterization.

Bio: Xudong Chen is an Associate Professor in the Department of Electrical and Systems Engineering at Washington University in St. Louis. He obtained the B.S. degree in Electronic Engineering from Tsinghua University, Beijing, China, in 2009, and the Ph.D. degree in Electrical Engineering from Harvard University, Cambridge, Massachusetts, in 2014. He is an awardee of the 2020 Air Force Young Investigator Program, a recipient of the 2021 NSF Career Award, the recipient of the 2021 Donald P. Eckman Award, and the recipient of the 2023 A.V. Balakrishnan Early Career Award.

His current research interests are in the area of control theory, stochastic processes, optimization, network science, and their applications.