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| HAL : hal-00338778, version 2 |
| arXiv : 0811.2335 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (14-11-2008) | v2 (28-11-2008) |
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| A continuous semigroup of notions of independence between the classical and the free one |
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| Florent Benaych-Georges 1, 2Thierry Lévy 3 |
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| (14/11/2008) |
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| In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These notions are related to the liberation process introduced by D. Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence. |
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| 1 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| 2 : | Centre de Mathématiques Appliquées (CMAP) |
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CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X |
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| 3 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris |
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| Domaine | : | Mathématiques/Probabilités |
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| Free Probability – Independence – Random Matrices – Unitary Brownian Motion – Convolution – Cumulants |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00338778, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00338778 | |
| oai:hal.archives-ouvertes.fr:hal-00338778 | |
| Contributeur : Thierry Lévy | |
| Soumis le : Vendredi 28 Novembre 2008, 11:49:17 | |
| Dernière modification le : Vendredi 28 Novembre 2008, 14:28:10 | |
