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Maurice Duits: Global fluctuations for eigenvalues of random matrices

Tid: On 2017-09-20 kl 15.15 - 16.15

Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Medverkande: Maurice Duits (KTH)

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Abstract: Starting from the classical example of the Gaussian Unitary Ensemble, the purpose of the talk is to provide an overview of various recent studies on global fluctuations of eigenvalues of random matrices and related models. The emphasis will be on Gaussian fields that appear in the asymptotic behavior of fluctuations of counting statistics. One example is the two dimensional massless Gaussian free field that describes the fluctuations for time dependent random matrices and the joint spectra for sub-matrices of GUE matrices. Also some basic models that witness a transition from random matrix type of statistics to Poissonian statistics will be discussed. The talk aims for a wide audience.