Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

Tiefeng Jiang

doi:10.1007/s00440-008-0146-x

Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

Tiefeng Jiang

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.

Original language	English (US)
Pages (from-to)	221-246
Number of pages	26
Journal	Probability Theory and Related Fields
Volume	144
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-008-0146-x
State	Published - May 2009

Bibliographical note

Funding Information:
Supported in part by NSF #DMS-0449365.

Keywords

Eigenvalue
Empirical distribution
Haar measure
Largest eigenvalue
Limiting distribution
Random matrix

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10.1007/s00440-008-0146-x

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abstract = "We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.",

keywords = "Eigenvalue, Empirical distribution, Haar measure, Largest eigenvalue, Limiting distribution, Random matrix",

author = "Tiefeng Jiang",

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N1 - Funding Information: Supported in part by NSF #DMS-0449365.

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Y1 - 2009/5

N2 - We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.

AB - We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.

KW - Eigenvalue

KW - Empirical distribution

KW - Haar measure

KW - Largest eigenvalue

KW - Limiting distribution

KW - Random matrix

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

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ER -

Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

Abstract

Bibliographical note

Keywords

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