Title: How large is the norm of a random matrix?
Abstract: Nonasymptotic estimates on the spectral norm of random matrices have proved to be indispensable in many problems in statistics, computer science, signal processing, and information theory. The noncommutative Khintchine inequality and its recent matrix concentration analogues are widely used in this context. Unfortunatly, such simple bounds fail to be sharp in many natural examples. In this talk, I will discuss new bounds on the norm of random matrices with independent entries that are
(provably) sharp in almost all cases of practical interest. Beside providing a substantial improvement on previously known results, the proof of these bounds is surprisingly illuminating and effectively explains when and why the norm of a random matrix is large. I will also discuss a more general conjecture whose resolution would provide a sharp version of the noncommutative Khintchine bound. No prior knowledge of random matrix theory will be assumed. (Joint work with Afonso Bandeira)
Biography: Ramon van Handel is an Assistant Professor in the ORFE Department and an associated faculty member in the Program for Applied and Computational Mathematics at Princeton University. His core research interests are in probability theory and related fields, and in their applications in science, engineering, and mathematics. He received the PhD degree from the California Institute of Technology in 2007, and joined the Princeton faculty in 2009. Selected honors include the NSF CAREER award and a PECASE award, the SICON paper prize from SIAM, the Princeton University Graduate Mentoring Award, and several Excellence in Teaching awards.