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Random Spectral Distributions

In: Interacting Stochastic Systems

Author

Listed:
  • Friedrich Götze

    (Universität Bielefeld, Fakultät für Mathematik)

  • Franz Merkl

    (University of Leiden, Department of Mathematics)

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.

Suggested Citation

  • Friedrich Götze & Franz Merkl, 2005. "Random Spectral Distributions," Springer Books, in: Jean-Dominique Deuschel & Andreas Greven (ed.), Interacting Stochastic Systems, pages 181-205, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27110-9_9
    DOI: 10.1007/3-540-27110-4_9
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