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Jan Nagel: Sum rules via large deviations

Tid: Ti 2018-01-23 kl 15.15 - 16.15

Plats: Room F11, KTH

Medverkande: Jan Nagel

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Abstract: We show a large deviation principle for the weighted spectral measure of random matrices corresponding to a general potential. Unlike for the empirical eigenvalue distribution, the speed reduces to n and the rate function contains a contribution of eigenvalues outside of the limit support. As an application, this large deviation principle yields a probabilistic proof of the celebrated Killip-Simon sum rule: a remarkable relation between the entries of a Jacobi-operator and its spectral measure. The talk is based on joint works with Fabrice Gamboa and Alain Rouault.