[Ml-stat-talks] SAS Fall 2014: Roots of polynomials and probabilistic applications

Ramon van Handel rvan at Princeton.EDU
Tue Sep 9 17:40:30 EDT 2014


Dear all,

Apologies for sending out a string in announcements in a row (Blackboard 
lectures by Mossel this Friday, the new probability seminar series, ...) 
we have several interesting activities this semester.

As we have done in the past, we will be running the stochastic analysis 
seminar as an informal course on a topic that we do not cover in the 
curriculum.  Due to interest from various people, we will be looking at 
the use of roots of polynomials as an unexpected tool in some 
probabilistic problems.  This should be of particular interest to 
probabilists and theoretical computer scientists, and also to 
statisticians and machine learners interested in new tools.

As usual, up-to-date information on the SAS will be posted here: 
http://orfe.princeton.edu/events/stochastic-analysis-seminar/details
I include a full announcement below.  Anyone is most welcome to participate.

Best regards,  -- Ramon

----

Fall 2014: Roots of polynomials and probabilistic applications

Understanding the roots of polynomials seems far from a probabilistic issue, 
yet has recently appeared as an important technique in various unexpected 
problems in probability as well as in theoretical computer science.  As an 
illustration of the power of such methods, these informal lectures will work 
through two settings where significant recent progress was enabled using this 
idea.  The first is the proof of the Kadison-Singer conjecture by using roots 
of polynomials to study the norm of certain random matrices.  The second is the 
proof that determinantal processes, which arise widely in probability theory, 
exhibit concentration of measure properties.  No prior knowledge of these 
topics will be assumed.

Time and location: Thursdays, 4:30-6:00, Sherrerd Hall 101.
The first lecture will be on September 18.

References:

* A. W. Marcus, D. A. Spielman,, N. Srivastava, Interlacing families I / II 
http://arxiv.org/abs/1304.4132
http://arxiv.org/abs/1306.3969

* Notes by T. Tao
http://terrytao.wordpress.com/2013/11/04/real-stable-polynomials-and-the-kadison-singer-problem/

* Notes by N. K. Vishnoi
http://research.microsoft.com/en-us/um/people/nvishno/Site/Publications_files/ZerosIntro.pdf

* Borcea, Branden, and Liggett, "Negative dependence and the geometry of 
polynomials."
http://www.ams.org/journals/jams/2009-22-02/S0894-0347-08-00618-8/S0894-0347-08-00618-8.pdf

* Pemantle and Peres, "Concentration of Lipschitz functionals of 
determinantal and other strong Rayleigh measures."
http://arxiv.org/abs/1108.0687


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