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| HAL : hal-00383512, version 1 |
| DOI : 10.1007/s10255-006-0306-7 |
| Fiche détaillée |  Récupérer au format |
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| Acta Mathematicae Applicatae Sinica / Acta Mathematicae Applicatae Sinica English Series 22, 2 (2006) 297-312 |
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| On the Spectral Distribution of Gaussian Random Matrices |
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| Bernard Delyon 1Jian-Feng Yao 1 |
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| (2006) |
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| We consider the empirical spectral distribution (ESD) of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotach approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O(n-1) to the Wigner distribution function uniformly on every compact intervals [u, v] within the limiting support (-1, 1). Furthermore, the variance of the ESD for such an interval is proved to be (πn)-2 log n asymptotically which surprisingly enough, does not depend on the details (e. g. length or location) of the interval. This property allows us to determine completely the covariance function between the values of the ESD on two intervals |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Domaine | : | Mathématiques/Statistiques |
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| Convergence rate – random matrices – empirical spectral distribution – Wigner distribution |
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| hal-00383512, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00383512 | |
| oai:hal.archives-ouvertes.fr:hal-00383512 | |
| Contributeur : Dominique Hervé | |
| Soumis le : Mercredi 13 Mai 2009, 09:51:35 | |
| Dernière modification le : Mercredi 13 Mai 2009, 09:51:35 | |
