Precise asymptotics for beta ensembles

Xingyuan Zeng () and Zhenting Hou
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Xingyuan Zeng: Central South University
Zhenting Hou: Central South University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 3, 383-404

Abstract: Abstract We consider the extremal (largest and smallest) eigenvalues of random matrices in the β-Hermite and β-Laguerre ensembles. Using the general β Tracy-Widom law together with Ledoux and Rider’s small deviation inequalities for β-ensembles, we obtain some precise asymptotic results in both settings. This complements Su’s results for the largest eigenvalue of Gaussian and Laguerre unitary ensembles.

Keywords: Extremal eigenvalues; β-ensembles; general β Tracy-Widom law; small deviation inequalities (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0020-0

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