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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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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DOI: https://doi.org/10.1007/978-3-319-17674-1_5
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