Talk: Ioana Dumitriu
Spectra of regular graphs and hypergraphs: theory and applications
University of California, San Diego
Properties of large networks are central to many machine learning and data science applications, from clustering to coding theory and matrix completion. Large random regular and quasi-regular graphs are well-known examples of expanders, graphs with particularly good connectivity and which have been successfully used to model large networks for decades; recently, the machine learning community has become interested in the study of regular and uniform hypergraphs as well. Although these random graph structures are very useful in practice, their spectral statistics (which control some of their crucial connectivity properties) have only recently started to become well-understood. Following the seminal work of Friedman and Bordenave on the spectral gap of random regular random graphs, we have extended their methods to the study of random bipartite biregular graphs and, through a very natural bijection, to random regular, uniform hypergraphs. I will present some of these results and mention some ongoing projects. This is joint work with Gerandy Brito, Kameron Harris, and Yizhe Zhu.