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"Universality in random matrix theory"
Wednesday, 22. Feb 2017
Video-Recording for any system with MP4-support
- Video.mp4 (ca.391 Mb)
15:15 – 16:20
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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