Right tail asymptotic expansion of Tracy-Widom beta laws (Q2920377)
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scientific article; zbMATH DE number 6094188
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Right tail asymptotic expansion of Tracy-Widom beta laws |
scientific article; zbMATH DE number 6094188 |
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16 October 2012
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Gaussian Ensembles
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Tracy-Widom laws
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Large deviations
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Random Matrices
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0.93569934
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0.8823887
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0.85975266
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0.85055906
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0.84724414
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0.8439608
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Right tail asymptotic expansion of Tracy-Widom beta laws (English)
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The authors consider Gaussian \(\beta\) matrix ensembles (G\(\beta\)E), \(\;\beta > 0,\;\) in which case it is known [\textit{J. A. Ramirez, B. Rider} and \textit{B. Virag}, ``Beta ensembles, stochastic Airy process, and a diffusion'', preprint (2006), \url{arXiv:math.FA/0609451}] that the maximal eigenvalue converges to a beta Tracy Widom law TW\(_\beta(s).\;\) In this paper, the asymptotics of these laws are studied in detail, as \(\;s \rightarrow \infty\;\) (right tail), using the large deviation of the maximal eigenvalue in the G\(\beta\)E, which is computed.
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