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
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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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