Probability Seminar
Wednesday, January 20, 2016, 11:15am, R. J. Reynolds Auditorium, Fuqua
Ramon van Handel (Princeton)
The norm of structured random matrices

Abstract:

Understanding the spectral norm of random matrices is a problem of basic interest in several areas of pure and applied mathematics. While the spectral norm of classical random matrix models is well understood, existing methods almost always fail to be sharp in the presence of nontrivial structure. In this talk, I will discuss new bounds on the norm of random matrices with independent entries that are sharp under mild conditions. These bounds shed significant light on the nature of the problem, and make it possible to easily address otherwise nontrivial phenomena such as the phase transition of the spectral edge of random band matrices. I will also discuss some conjectures whose resolution would complete our understanding of the underlying probabilistic mechanisms.

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