### Abstract

We study the spectral measure of Gaussian Wigner's matrices and prove that it satisfies a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner's semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about Voiculescu's non commutative entropy.

Original language | English (US) |
---|---|

Pages (from-to) | 517-542 |

Number of pages | 26 |

Journal | Probability Theory and Related Fields |

Volume | 108 |

Issue number | 4 |

State | Published - Aug 1997 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Statistics and Probability

### Cite this

*Probability Theory and Related Fields*,

*108*(4), 517-542.

**Large deviations for Wigner's law and Voiculescu's non-commutative entropy.** / Ben Arous, G.; Guionnet, A.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 108, no. 4, pp. 517-542.

}

TY - JOUR

T1 - Large deviations for Wigner's law and Voiculescu's non-commutative entropy

AU - Ben Arous, G.

AU - Guionnet, A.

PY - 1997/8

Y1 - 1997/8

N2 - We study the spectral measure of Gaussian Wigner's matrices and prove that it satisfies a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner's semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about Voiculescu's non commutative entropy.

AB - We study the spectral measure of Gaussian Wigner's matrices and prove that it satisfies a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner's semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about Voiculescu's non commutative entropy.

UR - http://www.scopus.com/inward/record.url?scp=0031499009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031499009&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031499009

VL - 108

SP - 517

EP - 542

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -