Seminars & Colloquia Calendar
The dimension-free structure of nonhomogeneous random matrices
Ramon Van Handel - Princeton University
Location: Hill 705
Date & time: Thursday, 18 October 2018 at 12:00PM - 1:00PM
Abstract: 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. More generally, we provide optimal dimension-independent estimates on the Schatten norms of random matrices with independent Gaussian entries. These results not only settle some basic questions in this area, but also provide significant insight on what such matrices look like and how they behave.