Mathematics Colloquium

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Universality of Random Matrices and Dyson Brownian Motion

Speaker: Horng-Tzer Yau, Harvard

Location: Warren Weaver Hall 1302

Date: Monday, December 7, 2009, 3:45 p.m.

Synopsis:

The universality for eigenvalue spacing distributions is a central question in the random matrix theory.

In this talk, we introduce a new general approach based on comparing the Dyson Brownian motion with a new related dynamics, the local relaxation flow. This method can be applied to prove the universality for the eigenvalue spacing distributions for the symmetric, hermitian, self‐dual quaternion matrices and the real and complex Wishart matrices. A central tool in this approach is to estimate the entropy flow via the logarithmic Sobolev inequality.