A permutation model for free random variables and its classical analogue

Abstract : In this paper, we generalize a permutation model for free random variables which was first proposed by Biane in \cite{biane}. We also construct its classical probability analogue, by replacing the group of permutations with the group of subsets of a finite set endowed with the symmetric difference operation. These constructions provide new discrete approximations of the respective free and classical Wiener chaos. As a consequence, we obtain explicit examples of non random matrices which are asymptotically free or independent. The moments and the free (resp. classical) cumulants of the limiting distributions are expressed in terms of a special subset of (noncrossing) pairings. At the end of the paper we present some combinatorial applications of our results.
Type de document :
Pré-publication, Document de travail
13 pages, to appear in Pacific Journal of Mathematics. 2009
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00220460
Contributeur : Ion Nechita <>
Soumis le : mercredi 11 février 2009 - 14:40:02
Dernière modification le : jeudi 27 avril 2017 - 09:46:20
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 17:09:35

Fichiers

perm.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00220460, version 3
  • ARXIV : 0801.4229

Collections

Citation

Florent Benaych-Georges, Ion Nechita. A permutation model for free random variables and its classical analogue. 13 pages, to appear in Pacific Journal of Mathematics. 2009. <hal-00220460v3>

Partager

Métriques

Consultations de
la notice

209

Téléchargements du document

68