Extreme Eigenvalue Distributions of Sparse Random Graphs - Jiaoyang Huang

Explore the fascinating world of extreme eigenvalue distributions in sparse random graphs through this comprehensive lecture by Jiaoyang Huang, a member of the School of Mathematics at the Institute for Advanced Study. Delve into topics such as empirical eigenvalue distribution, edge expansion constant, and Roman routing graphs. Examine the universality of distributions, numerical simulations, and the bias towards the negative axis. Gain insights into Gaussian and circular ensembles, spectral result resolution, and the concept of simple switching. Discover how these mathematical concepts apply to real-world scenarios and contribute to the field of mathematical physics.

Introduction
Empirical eigenvalue distribution
Edge expansion constant
cheekers constant
Roman routing graphs
Bipartite routing graphs
Gaussian or circular ensemble
Plot eigenvalue distribution
Distributions are universal
Numerical simulation
Bias towards negative axis
First result
Second result
Proof ingredients
Gaussian distribution
Spectral result resolution
Spectral scale of ETA
Gaussian circular example
Symmetry
Simple switching
High movement