Ramanujan Property and Edge Universality of Random Regular Graphs

This lecture explores the Ramanujan property and edge universality in the context of random regular graphs. The Ramanujan property concerns the optimal spectral gap in regular graphs, which has implications for expander graphs and network design. Edge universality refers to the universal behavior of the extremal eigenvalues of such graphs, analogous to results in random matrix theory. The talk will present recent theoretical developments and open problems in this area.