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A Remark on Hypercontractivity and Tail Inequalities for the Largest Eigenvalues of Random Matrices

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1832)

Abstract

We point out a simple argument relying on hypercontractivity to describe tail inequalities on the distribution of the largest eigenvalues of random matrices at the rate given by the Tracy–Widom distribution. The result is illustrated on the known examples of the Gaussian and Laguerre unitary ensembles. The argument may be applied to describe the generic tail behavior of eigenfunction measures of hypercontractive operators.

Keywords

  • Random Matrice
  • Random Matrix
  • Hermite Polynomial
  • Logarithmic Sobolev Inequality
  • Markov Semigroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2003 Springer-Verlag Berlin Heidelberg

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Ledoux, M. (2003). A Remark on Hypercontractivity and Tail Inequalities for the Largest Eigenvalues of Random Matrices. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_14

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  • DOI: https://doi.org/10.1007/978-3-540-40004-2_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20520-3

  • Online ISBN: 978-3-540-40004-2

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