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Universality of general β-ensembles
(Duke University Press, 2014)
We prove the universality of the β-ensembles with convex analytic potentials and for any β>0; that is, we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian ...
Bulk universality of general β-ensembles with non-convex potential
(AIP Publishing, 2012-09)
We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, ...
Fixed Energy Universality for Generalized Wigner Matrices
(Wiley-Blackwell, 2015)
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 ...