Central Limit Theorems for the Brownian motion on large unitary groups

Abstract : In this paper, we are concerned with the large N limit of linear combinations of the entries of a Brownian motion on the group of N by N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one. Various scales of time and various initial distribution are concerned, giving rise to various limit processes, related to the geometric construction of the unitary Brownian motion. As an application, we propose a quite short proof of the asymptotic Gaussian feature of the linear combinations of the entries of Haar distributed random unitary matrices, a result already proved by Diaconis et al.
Type de document :
Pré-publication, Document de travail
14 pages. 2009
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https://hal.archives-ouvertes.fr/hal-00374929
Contributeur : Florent Benaych-Georges <>
Soumis le : mardi 21 juin 2011 - 15:11:06
Dernière modification le : lundi 29 mai 2017 - 14:23:32
Document(s) archivé(s) le : jeudi 22 septembre 2011 - 02:25:43

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  • HAL Id : hal-00374929, version 4
  • ARXIV : 0904.1681

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Florent Benaych-Georges. Central Limit Theorems for the Brownian motion on large unitary groups. 14 pages. 2009. <hal-00374929v4>

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