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Pré-Publication, Document De Travail Année : 2009

A permutation model for free random variables and its classical analogue

Résumé

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.
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Dates et versions

hal-00220460 , version 1 (28-01-2008)
hal-00220460 , version 2 (19-03-2008)
hal-00220460 , version 3 (11-02-2009)

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Florent Benaych-Georges, Ion Nechita. A permutation model for free random variables and its classical analogue. 2009. ⟨hal-00220460v3⟩
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