Fall 2014: Roots of polynomials and probabilistic applications
Welcome back to the stochastic analysis seminar! We resume this semester with an unusual but exciting topic: the geometry of roots of polynomials and their 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 (note different location than last year).
The first lecture will be on September 18.
Notes from the lectures, schedule changes and any other announcements will be posted on this blog.
- A. W. Marcus, D. A. Spielman, N. Srivastava, “Interlacing families I/II”
- Notes by T. Tao
- Notes by N. K. Vishnoi
- J. Borcea, P. Brändén, T. M. Liggett, “Negative dependence and the geometry of polynomials”
- R. Pemantle and Y. Peres, “Concentration of Lipschitz functionals of determinantal and other strong Rayleigh measures”