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The dimension-free structure of nonhomogeneous random matrices

Geometric functional analysis and applications November 13, 2017 - November 17, 2017

November 16, 2017 (04:15 PM PST - 05:15 PM PST)
Speaker(s): Ramon Van Handel (Princeton University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • random matrices

  • noncommutative probability

  • Schatten norms

  • nonasymptotic bounds

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

16-Van Handel

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, 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.

Supplements
30103?type=thumb Van Handel Notes 869 KB application/pdf Download
Video/Audio Files

16-Van Handel

H.264 Video 16-Van_Handel.mp4 489 MB video/mp4 rtsp://videos.msri.org/data/000/030/025/original/16-Van_Handel.mp4 Download
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