On bi-free De Finetti theorems

Amaury Freslon; Moritz Weber

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arXiv · 1501.05124

On bi-free De Finetti theorems

Amaury Freslon·Moritz Weber

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Abstract

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.

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BibTeX RIS

Amaury Freslon, Moritz Weber. 2015-07-21. On bi-free De Finetti theorems. https://arxiv.org/abs/1501.05124

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