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      MATHEMATICS COLLOQUIUM

 

                                    "Universality in random matrix theory"

 

        Date:

    Download-files:

      Time:

 Wednesday, 22. Feb 2017

    Video-Recording for any system with MP4-support

 

       - Video.mp4 (ca.391 Mb)

 

 15:15 – 16:20

 

                                       

                                                             Arno Kuijlaars

                                         (Katholieke Universiteit Leuven, Belgium)

 

Abstract :

Eigenvalues of large random matrices have a remarkable behavior as the size of the

matrices tends to infinity. The local repulsion of eigenvalues leads to microscopic

limit laws that are independent of the fine details of the random matrix model.

This universality phenomenon was observed by Wigner in the 1950s and proved by

mathematicians in great generality since the 1990s.

 

Deviations from universality correspond to phase transitions in limiting eigenvalue

behavior that can be analyzed with nonlinear special functions: the Painlevé transcendents.

For example the breaking of a spectral gap corresponds to a special solution of the

Painlevé II equation.

 

In the talk I will give an overview of these developments. I will also discuss the more

recently discovered universal behavior for eigenvalues and singular values of products

of random matrices.

 

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