The dimension-free structure of nonhomogeneous random matrices
Geometric functional analysis and applications November 13, 2017 - November 17, 2017
Location: MSRI: Simons Auditorium
60B20 - Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
46B09 - Probabilistic methods in Banach space theory [See also 60Bxx]
What does the spectrum of a random matrix look like when the entries can have an arbitrary variance pattern? Such questions, which are of interest in several areas of pure and applied mathematics, are largely orthogonal to problems of classical random matrix theory. For example, one might ask the following basic question: when does an infinite matrix with independent Gaussian entries define a bounded operator on l_2? In this talk, I will describe recent work with Rafal Latala and Pierre Youssef in which we completely answer this question, settling an old conjecture of Latala. More generally, we provide optimal estimates on the Schatten norms of random matrices with independent Gaussian entries. These results not only answer some basic questions in this area, but also provide significant insight on what such matrices look like and how they behave.
Van Handel Notes
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