 |
|
|
|
| HAL : hal-00531668, version 1 |
| arXiv : 1011.0299 |
| DOI : 10.1016/j.jmva.2011.11.006 |
| Fiche détaillée |  Récupérer au format |
|
|
| Journal of Multivariate Analysis 106 (2012) 17-35 |
|
|
|
|
| Large Deviations for Random Matricial Moment Problems |
|
|
| Jan NagelJens Wagener |
|
|
| (04/2012) |
|
|
|
| We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \rightarrow \infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\times p$ matrices. Then we lift a random element of $\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP on Carathéodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut de Mathématiques de Toulouse (IMT) |
|
|
|
Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 |
|
|
| 2 : | Laboratoire de Mathématiques de Versailles (LM-Versailles) |
|
|
|
CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Probabilités |
|
|
| Random matrices – moments spaces – canonical moments – large deviations – Carathéodory functions – Schur functions |
|
|
|
| Lien vers le texte intégral : |
|
| http://fr.arXiv.org/abs/1011.0299 |
| hal-00531668, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00531668 | |
| oai:hal.archives-ouvertes.fr:hal-00531668 | |
| Contributeur : Alain Rouault | |
| Soumis le : Mercredi 3 Novembre 2010, 14:40:11 | |
| Dernière modification le : Mercredi 27 Février 2013, 11:22:34 | |
