Universality of Random Matrices and Dyson Brownian Motion

Universality of Random Matrices and Dyson Brownian Motion

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H-T Yau, Harvard University
Jadwin Hall 343

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.