# How much can the eigenvalues of a random Hermitian matrix fluctuate?

@article{Claeys2021HowMC, title={How much can the eigenvalues of a random Hermitian matrix fluctuate?}, author={Tom Claeys and Benjamin Fahs and Gaultier Lambert and Christian Webb}, journal={Duke Mathematical Journal}, year={2021} }

The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in the setting of one-cut regular unitary invariant ensembles of random Hermitian matrices -- the Gaussian Unitary Ensemble being the prime example of such an ensemble. Our approach to this question combines extreme value theory of log-correlated stochastic…

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