Fixed Energy Universality for Generalized Wigner Matrices
By P. Bourgade, L. Erdős, Horng-Tzer Yau, Jun Yin. 2014
136 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b977fe41dabfd610ee0305d6ff9522434177c091
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In Discrete Mathematics and Combinatorics
In Mathematical Physics
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Citations in the corpus
- A Dynamical Approach to Random Matrix Theory (2017, background): “[26] Consider a complex Hermitian (respectively, real symmetric) generalized Wigner matrix with moment condition (18.”
- Transition from Tracy–Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs (2017, result): “near statistics, after normalizing by p1=2, converge to a Gaussian random variable. A three-step dynamical approach to the local statistics of random matrices has been developed in a series of papers [2,8,18,22{28,41,42]. This strategy is as follows. The work of H.-T. Y. is partially supported by NS”
- Random matrices: tail bounds for gaps between eigenvalues (2015, background): “An analogue of (2) for real smooth ensembles, with the exponent k 2 replaced by k ( k + 1) / 2, was established in [4, Appendix B].”
- Eigenvector Statistics of Sparse Random Matrices (2016, methodology): “With this as input and combining with the rigidity estimates of eigenvalues from [5], we analyze the eigenvector moment flow of Dyson Brownian motion following the approach developed in [6].”