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Mathematical Physics of Quantum Mechanics pp 351–364Cite as

Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles

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Part of the book series: Lecture Notes in Physics ((LNP,volume 690))

Abstract

The two archetypal ensembles of random matrices are Wigner real symmetric (Hermitian) random matrices and Wishart sample covariance real (complex) random matrices. In this paper we study the statistical properties of the largest eigenvalues of such matrices in the case when the second moments of matrix entries are infinite. In the first two subsections we consider Wigner ensemble of random matrices and its generalization – band random matrices.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, CA, Davis, 95616, USA

    Alexander Soshnikov

Authors
  1. Alexander Soshnikov
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Editor information

Editors and Affiliations

  1. Département de Mathématiques, Université du Sud Toulon Var Centre de physique théorique, F-83957 La Garde Cedex, 20132, France

    Joachim Asch

  2. Institut Fourier Université Grenoble 1, 38402 Saint-Martin-d’Hères Cedex, 74, France

    Alain Joye

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Soshnikov, A. (2006). Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_26

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