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Statistical mechanics approach to the random matrix models

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Mathematics and Physics of Anderson localization: 50 Years After

We consider hermitian, real symmetric and symplectic matrix models with real analytic potentials and present some analogue of the mean-field approximation method to study their partition functions in the multi-cut regime. Then we discuss recent results on the asymptotic behavior of the characteristic functional of linear eigenvalue statistics, obtained by this method, in particular, non gaussian behavior of the characteristic functional in the multi-cut regime. The applications to the proof of the universality conjecture for real symmetric and symplectic matrix models will be also discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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