[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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