IFML Seminar: 03/07/25 - Spectral Norm of Random Matrices and Tensors

Abstract: In the first part of this presentation, I'll present a non-asymptotic bound for the spectral norm of a Gaussian series random matrix and show an application (by Bansal, Jiang, Meka) of this result to the Matrix Spencer Conjecture. In the second part, I'll present a non-asymptotic bound for the spectral norm of a random tensor with independent entries and discuss prior results on this problem.

References: 
(1) A.S. Bandeira, M.T. Boedihardjo, R. van Handel, Matrix Concentration Inequalities and Free Probability, Inventiones Mathematicae (2023)
(2) N. Bansal, H. Jiang, R. Meka, Resolving Matrix Spencer Conjecture up to Poly-logarithmic Rank, STOC (2023)
(3) M.T. Boedihardjo, Injective Norm of Random Tensors with Independent Entries, arxiv 2412.21193

Bio: March Boedihardjo is an assistant professor at Michigan State University.