### Abstract

A large deviation theorem is obtained for a certain sequence of random measures which includes the empirical eigenvalue distribution of Wishart matrices, as the matrix size tends to infinity. The rate function is convex and one of its ingredients is the logarithmic energy. In the case of the singular Wishart matrix, the limit distribution has an atom.

Original language | English |
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Pages (from-to) | 633-646 |

Number of pages | 14 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 1 |

Issue number | 4 |

Publication status | Published - Oct 1998 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Mathematical Physics
- Statistics and Probability
- Statistical and Nonlinear Physics

### Cite this

**Eigenvalue density of the wishart matrix and large deviations.** / Hiai, Fumio; Petz, Dénes.

Research output: Contribution to journal › Article

*Infinite Dimensional Analysis, Quantum Probability and Related Topics*, vol. 1, no. 4, pp. 633-646.

}

TY - JOUR

T1 - Eigenvalue density of the wishart matrix and large deviations

AU - Hiai, Fumio

AU - Petz, Dénes

PY - 1998/10

Y1 - 1998/10

N2 - A large deviation theorem is obtained for a certain sequence of random measures which includes the empirical eigenvalue distribution of Wishart matrices, as the matrix size tends to infinity. The rate function is convex and one of its ingredients is the logarithmic energy. In the case of the singular Wishart matrix, the limit distribution has an atom.

AB - A large deviation theorem is obtained for a certain sequence of random measures which includes the empirical eigenvalue distribution of Wishart matrices, as the matrix size tends to infinity. The rate function is convex and one of its ingredients is the logarithmic energy. In the case of the singular Wishart matrix, the limit distribution has an atom.

UR - http://www.scopus.com/inward/record.url?scp=0000032203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000032203&partnerID=8YFLogxK

M3 - Article

VL - 1

SP - 633

EP - 646

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

SN - 0219-0257

IS - 4

ER -