Annales Mathématiques
Blaise Pascal
no. 1
On bi-free De Finetti theorems
Amaury Freslon1 ; Moritz Weber1
1 Saarland University, Fachbereich Mathematik, Postfach 151159, 66041 Saarbrücken, Germany
Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 1, pp. 21-51.

We investigate possible generalizations of the de Finetti theorem to bi-free probability. We first introduce a twisted action of the quantum permutation groups corresponding to the combinatorics of bi-freeness. We then study properties of families of pairs of variables which are invariant under this action, both in the bi-noncommutative setting and in the usual noncommutative setting. We do not have a completely satisfying analogue of the de Finetti theorem, but we have partial results leading the way. We end with suggestions concerning the symmetries of a potential notion of n-freeness.

Publié le :
DOI : 10.5802/ambp.353
Classification : 46L54, 46L53, 20G42
Mots clés : Quantum groups, free probability, De Finetti theorem

Amaury Freslon 1 ; Moritz Weber 1

1 Saarland University, Fachbereich Mathematik, Postfach 151159, 66041 Saarbrücken, Germany 
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Amaury Freslon; Moritz Weber. On bi-free De Finetti theorems. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 1, pp. 21-51. doi : 10.5802/ambp.353. https://ambp.centre-mersenne.org/articles/10.5802/ambp.353/

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