Fixed Energy Universality for Generalized Wigner Matrices |
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| Authors: | Paul Bourgade Laszlo Erdős Horng‐Tzer Yau Jun Yin |
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| Institution: | 1. Courant Institute, New York, NY, USA;2. Institute of Science and Technology Austria, Klosterneuburg, Austria;3. Harvard University, Cambridge, MA, USA;4. University of Wisconsin‐Madison, Madison, WI, USA |
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| Abstract: | We prove the Wigner‐Dyson‐Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.© 2016 Wiley Periodicals, Inc. |
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