### Abstract

It is shown that the empirical eigenvalue distribution of suitably distributed random unitary matrices satisfies the large deviation principle as the matrix size goes to infinity. The primary term of the rate function is the logarithmic energy (or the minus sign of Voiculescu's free entropy). Examples of random unitaries are also discussed, one of them is related to the work of Gross and Witten in quantum physics.

Original language | English |
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Pages (from-to) | 71-85 |

Number of pages | 15 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 36 |

Issue number | 1 |

Publication status | Published - Jan 2000 |

### Fingerprint

### Keywords

- Eigenvalue density
- Large deviation
- Logarithmic energy
- Random unitary matrix

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices.** / Hiai, Fumio; Petz, D.

Research output: Contribution to journal › Article

*Annales de l'institut Henri Poincare (B) Probability and Statistics*, vol. 36, no. 1, pp. 71-85.

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TY - JOUR

T1 - A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices

AU - Hiai, Fumio

AU - Petz, D.

PY - 2000/1

Y1 - 2000/1

N2 - It is shown that the empirical eigenvalue distribution of suitably distributed random unitary matrices satisfies the large deviation principle as the matrix size goes to infinity. The primary term of the rate function is the logarithmic energy (or the minus sign of Voiculescu's free entropy). Examples of random unitaries are also discussed, one of them is related to the work of Gross and Witten in quantum physics.

AB - It is shown that the empirical eigenvalue distribution of suitably distributed random unitary matrices satisfies the large deviation principle as the matrix size goes to infinity. The primary term of the rate function is the logarithmic energy (or the minus sign of Voiculescu's free entropy). Examples of random unitaries are also discussed, one of them is related to the work of Gross and Witten in quantum physics.

KW - Eigenvalue density

KW - Large deviation

KW - Logarithmic energy

KW - Random unitary matrix

UR - http://www.scopus.com/inward/record.url?scp=0033632952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033632952&partnerID=8YFLogxK

M3 - Article

VL - 36

SP - 71

EP - 85

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 1

ER -