Spectrum of Random Graphs - Lecture 1

Explore the fundamental concepts of spectral analysis in random graphs through this graduate-level lecture from Kyoto University's Top Global Course series. Delve into the study of adjacency and Laplacian operators of finite random graphs and Cayley graphs of groups, beginning with an introduction to spectral measures and their continuity properties in relation to the Benjamini-Schramm topology. Examine the regularity properties of spectral measures within the context of quantum percolation, and investigate the convergence behavior of extremal eigenvalues in random graphs. Delivered by Professor Charles Bordenave from CNRS & Aix-Marseille University, this online lecture forms part of a comprehensive series presented in November 2021.