Outliers in Sparse Wigner Matrices

Explore the impact of sparsity on extreme eigenvalues in Wigner matrices with centered bounded entries in this 41-minute lecture. Delve into the emergence of outliers in the semi-circular law as sparsity increases, focusing on the Erdos-Renyi graph case to observe a phase transition. Learn about Wigner perturbations, BBP phase transition, general perturbation, concentration, and the threshold of emergence for outliers in random matrices. Gain insights from the joint work of Pierre Youssef and Konstantin Tikhomirov, presented at the Hausdorff Center for Mathematics.

Intro
Theorems
Wigner perturbations
BBP phase transition
General perturbation
Concentration
No outliers
Random matrices
Threshold of emergence