Graduate Student / Postdoc Seminar

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Universality in Random Matrix Theory

Speaker: Paul Bourgade

Location: Warren Weaver Hall 1302

Date: Friday, October 17, 2014, 1 p.m.

Synopsis:

Eugene Wigner stated the general hypothesis that the distribution of eigenvalue spacings of large complicated quantum systems is universal, in the sense that it depends only on the symmetry class of the physical system but not on other detailed structures. The simplest case for this hypothesis concerns large but finite dimensional matrices. I will explain some historical aspects random matrix theory, as well as recent techniques developed to prove eigenvalues and eigenvectors universality, for matrices with independent entries from all symmetry classes. The methods are both probabilist (random walks and coupling) and analytic (homogenization for parabolic PDEs with random coefficients).