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| HAL : hal-00578761, version 1 |
| arXiv : 1103.4693 |
| DOI : 10.1007/978-3-642-27461-9_9 |
| Fiche détaillée |  Récupérer au format |
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| Séminaire de Probabilités XLIV, Catherine Donati-Martin, Antoine Lejay, Alain Rouault (Ed.) (2012) 191-206 |
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| Spectral distribution of the free unitary Brownian motion: another approach |
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| Nizar Demni 1Taoufik Hmidi 1 |
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| (2012) |
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| We revisit the description provided by Ph. Biane of the spectral measure of the free unitary Brownian motion. We actually construct for any $t \in (0,4)$ a Jordan curve $\gamma_t$ around the origin, not intersecting the semi-axis $[1,\infty[$ and whose image under some meromorphic function $h_t$ lies in the circle. Our construction is naturally suggested by a residue-type integral representation of the moments and $h_t$ is up to a Möbius transformation the main ingredient used in the original proof. Once we did, the spectral measure is described as the push-forward of a complex measure under a local diffeomorphism yielding its absolute-continuity and its support. Our approach has the merit to be an easy yet technical exercise from real analysis. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Théorie ergodique Equations aux dérivées partielles |
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| Domaine | : | Mathématiques/Algèbres d'opérateurs Mathématiques/Analyse classique |
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| hal-00578761, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00578761 | |
| oai:hal.archives-ouvertes.fr:hal-00578761 | |
| Contributeur : Nizar Demni | |
| Soumis le : Jeudi 24 Mars 2011, 09:04:09 | |
| Dernière modification le : Jeudi 23 Août 2012, 11:25:49 | |
