PC Seminar: From graph limit theory to the eigenvectors of random matrices

Abstract: Graph limit theory has turned out to be a strong tool for various problems in extremal combinatorics, theory of random graphs, spectral graph theory, as it combines tools from analysis, probability theory, information theory. Furthermore, it can be used to develop methods for understanding the structure of certain random matrices. In the talk, we present our approach for the convergence of matrices (so-called action convergence), its relationship to the concepts of graph limits, and the way we can find convergent sequences of non-Hermitian random matrices, where all entries are independent. We also discuss how this theory can be applied for problems about eigenvectors of non-Hermitian random matrices. Joint work with Balázs Szegedy.

This is a seminar in our seminar series on Probability and Combinatorics (PC).