Speaker: Byron Chin (MIT)

Title: Structure of lower tails in sparse random graphs 

Abstract:

In 2011, Chatterjee and Varadhan proved a large deviations principle for the Erd\H{o}s--R\'enyi graph, $G(n,p)$, with constant edge density. One consequence of their result is a characterization of a typical random graph conditioned on having few triangles. In this talk, I will discuss recent work extending the characterization to sparse random graphs, i.e. $G(n,p)$ with vanishing edge density. The techniques connect to mean-field approximations and the hypergraph container method.