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• W3100651947 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." @default.
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• W3100651947 date "2009-09-01" @default.
• W3100651947 modified "2023-10-16" @default.
• W3100651947 title "A permutation model for free random variables and its classical analogue" @default.
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• W3100651947 doi "https://doi.org/10.2140/pjm.2009.242.33" @default.
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