### Abstract

Original language | English |
---|---|

Article number | 1750005 |

Number of pages | 49 |

Journal | Random Matrices: Theory and Applications |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 |

Externally published | Yes |

### Fingerprint

### Cite this

*Random Matrices: Theory and Applications*,

*6*(1), [1750005]. https://doi.org/10.1142/S2010326317500058

}

*Random Matrices: Theory and Applications*, vol. 6, no. 1, 1750005. https://doi.org/10.1142/S2010326317500058

**Sum rules and large deviations for spectral measures on the unit circle.** / Gamboa, F.; Nagel, J.H.; Rouault, A.

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

TY - JOUR

T1 - Sum rules and large deviations for spectral measures on the unit circle

AU - Gamboa, F.

AU - Nagel, J.H.

AU - Rouault, A.

PY - 2017

Y1 - 2017

N2 - This work is a companion paper of Gamboa, Nagel, Rouault (J. Funct. Anal. 2016). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two matrix models. The first one is the Gross-Witten ensemble. In the gapped regime we give a probabilistic interpretation of a Simon sum rule. The second matrix model is the Hua-Pickrell ensemble. Unlike the Gross-Witten ensemble the potential is here infinite at one point. Surprisingly, but as in the above mentioned paper, we obtain a completely new sum rule for the deviation to the equilibrium measure of the Hua-Pickrell ensemble. The extension to matrix measures is also studied.

AB - This work is a companion paper of Gamboa, Nagel, Rouault (J. Funct. Anal. 2016). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two matrix models. The first one is the Gross-Witten ensemble. In the gapped regime we give a probabilistic interpretation of a Simon sum rule. The second matrix model is the Hua-Pickrell ensemble. Unlike the Gross-Witten ensemble the potential is here infinite at one point. Surprisingly, but as in the above mentioned paper, we obtain a completely new sum rule for the deviation to the equilibrium measure of the Hua-Pickrell ensemble. The extension to matrix measures is also studied.

KW - math.PR

U2 - 10.1142/S2010326317500058

DO - 10.1142/S2010326317500058

M3 - Article

VL - 6

JO - Random Matrices: Theory and Applications

JF - Random Matrices: Theory and Applications

SN - 2010-3263

IS - 1

M1 - 1750005

ER -