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Spectral Properties of Wigner Matrices

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Book cover Correlated Random Systems: Five Different Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2143))

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Abstract

We review some recent results on the statistical properties of the spectrum of Wigner matrices. In particular, we discuss the local convergence of the density of states towards Wigner’s semicircle law, the rigidity of the eigenvalues of Wigner matrices and the universality of the local eigenvalue correlations.

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Acknowledgements

This work is partially supported by the ERC Starting Grant MAQD-240518. It is a pleasure to thank CIRM and the Chair Jean-Morlet Nicola Kistler for the hospitality.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Benjamin Schlein

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  1. Benjamin Schlein
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Correspondence to Benjamin Schlein .

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Editors and Affiliations

  1. Institut de Mathématiques de Marseille, Aix-Marseille Université CNRS, Marseille Cedex 13, France

    Véronique Gayrard

  2. Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

    Nicola Kistler

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Schlein, B. (2015). Spectral Properties of Wigner Matrices. In: Gayrard, V., Kistler, N. (eds) Correlated Random Systems: Five Different Methods. Lecture Notes in Mathematics, vol 2143. Springer, Cham. https://doi.org/10.1007/978-3-319-17674-1_5

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