Edge Universality for Non-Hermitian Random Matrices

Explore edge universality for non-Hermitian random matrices in this 49-minute lecture by Laszlo ERDOES from IST Klosterneuburg, Austria. Delve into topics such as eigenvalues of random matrices with independent entries, the circular law, and universality conjectures. Examine techniques for proving spectral universality, cusp universality for Hermitian Wigner-type matrices, and Girko's Hermitization. Learn about local law, classical smoothing inequalities, and smoothing in the transitional regime. Gain insights into the proof of non-Hermitian edge universality through a detailed sketch. This talk, part of the School and Workshop on Random Matrix Theory and Point Processes, offers a comprehensive overview of advanced concepts in random matrix theory.

Intro
Eigenvalues of random matrices with independent entries
The circular law
Universality Conjecture
Universality III: Theorem at the Edge
Techniques for Proving Spectral Universality incomplete overview
Cusp Universality for Hermitian Wigner-type matrices
Girko's Hermitization
Local Law for
Sketch of the proof of the non-Hermitian Edge universality
Classical Smoothing Inequalities
Smoothing in the Transitional Regime