Matrix Concentration and Universality - Working Seminar on HDP

Date: April 1, 2025

Time: 4:30PM - 5:30PM

Location: Blocker 302

Speaker: Tatiana Brailovskaya (Duke)

Description: In the latter half of the 20th century, extending scalar concentration inequalities to arbitrary Banach spaces has gained poplularity due to the implications for local geometry of these spaces. In 1990s, Lust-Piquard and Pisier intiated the study of matrix concentration by proving an analogue of the classical Khintchine inequality for matrices. This non-commutative Khinchine inequality paved the way for investigating spectral properties of random matrices with non-identical, non-independent entries, which are outside of the real of classical random matrix theory. Nowadays, there are numerous applications of matrix concentration in computer science and applied and pure mathematics. In this talk, I will discuss recent results concerning the spectrum of sums of independent random matrices with appropriate control on operator norms.