Institute of Mathematics


Modul:   MAT971  Stochastische Prozesse

Noncommutative Matrix Concentration Inequalities

Talk by Prof. Dr. Afonso Bandeira

Date: 24.11.21  Time: 17.15 - 18.15  Room: ETH HG G 19.1

Matrix Concentration inequalities for the spectrum of random matrices, such as Matrix Bernstein, have played an important role in many areas of pure and applied mathematics. These inequalities are intimately related to the celebrated noncommutative Khintchine inequality of Lust-Piquard and Pisier. In this talk we leverage ideas from Free Probability to remove the dimensional dependence in the noncommutative Khintchine in a range of instances, yielding sharp bounds in many settings of interest. As a byproduct we develop non-assymptotic matrix concentration inequalities that capture non-commutativity (or, to be more precise, ``freeness'').

Joint work with March Boedihardjo and Ramon van Handel, more information at arXiv:2108.06312 [math.PR].