[Ml-stat-talks] SAS Fall 2012: Random matrices

Ramon van Handel rvan at Princeton.EDU
Mon Sep 10 12:56:22 EDT 2012


Dear all,

As we did last fall, we aim to devote part of the Stochastic Analysis 
Seminar to an informal seminar course on a topic in contemporary 
probability that is not currently taught in the curriculum.

This fall, we will attempt an introduction to random matrix theory (see 
abstract at the bottom of this email).  This is a vast subject, so only 
some selected topics can be covered in a semester.  However, we will start 
at the beginning, and will see how far we get as the semester progresses.

Your friendly lecturers this semester will be Sebastien Bubeck, Rene 
Carmona, Philippe Rigollet and yours truly.  The lectures will be held on 
Thursdays from 4:30-6:00 starting September 20th in Bendheim Center 
classroom 103. Further details/updates will be posted at 
http://orfe.princeton.edu/sas .

As always, all are welcome. Looking forward to seeing you at the seminar!

    -- Ramon

PS: there will be no regular outside stochastic analysis seminar speakers 
this semester.  Outside speakers resume in the spring semester.


Fall 2012: Random matrices

Both the theory and applications of random matrices have attracted 
significant attention in recent years. In particular, much effort has gone 
into understanding the spectral properties of large random matrices, with 
applications ranging from statistical physics to signal processing to 
high-dimensional statistical inference.

The goal of these informal lectures is to provide a basic introduction to 
some selected results in random matrix theory. Potential topics include: 
Wigner matrices and the semicircle distribution; Wishart matrices and the 
Marcenko-Pastur distribution; asymptotics of the top and bottom singular 
values; fluctuations of linear eigenvalue statistics and of the top 
eigenvalue; Dyson Brownian motions and related topics. If time permits 
(which is unlikely) we will introduce some free probability.

Prerequisites: Probability at the level of ORF 526 is assumed.

Time and location: Thursdays, 4:30-6:00, Bendheim Center classroom 103. 
The first lecture will be on September 20.

Lecturers: S. Bubeck, R. Carmona, P. Rigollet, R. van Handel

References:

* G. W. Anderson, A. Guionnet, O. Zeitouni, "An Introduction to Random 
Matrices," Cambridge.

* Z. Bai and J. W. Silverstein, "Spectral Analysis of Large Dimensional 
Random Matrices," Springer.

* T. Tao, "Topics in Random Matrix Theory," AMS.

* R. Vershynin, "Introduction to the non-asymptotic analysis of random 
matrices," lecture notes.




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