Random Spectral Distributions

Friedrich Götze () and Franz Merkl ()
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Friedrich Götze: Universität Bielefeld, Fakultät für Mathematik
Franz Merkl: University of Leiden, Department of Mathematics

A chapter in Interacting Stochastic Systems, 2005, pp 181-205 from Springer

Abstract: Summary We review recent results and new methods for the distributions of spectra of random matrices and prove a kind of Mock-Gaussian behavior for eigenvalues of unitary random matrices (CUE), using creation and annihilation operators from quantum field theory. The result is non-asymptotic and plays a key role in establishing the relation between the local distribution of the zeros of the zeta function and the universal asymptotic local distribution of eigenvalues of unitary matrix ensembles.

Keywords: Zeta Function; Random Matrice; Random Matrix; Riemann Zeta Function; Random Matrix Theory (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27110-9_9

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DOI: 10.1007/3-540-27110-4_9

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