Spectrum of Random Graphs - Lecture 4

Explore the fourth lecture in a series on the spectrum of random graphs, delivered by Professor Charles Bordenave from CNRS and Aix-Marseille University as part of Kyoto University's Graduate School of Science Top Global Course Special Lectures. Delve into advanced mathematical concepts including spectral measures of adjacency and Laplacian operators in finite random graphs and Cayley graphs of groups. Learn about the continuity properties of these measures in relation to the Benjamini-Schramm topology, examine the regularity properties of spectral measures within the quantum percolation framework, and understand the convergence behavior of extremal eigenvalues in random graphs. Originally presented online in November 2021, this two-hour lecture forms part of a comprehensive mathematical exploration of graph theory and its applications.