We showthat the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen 'exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation ...

The extended de Finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to ...

We introduce 'braidability' as a new symmetry for infinite sequences of noncommutative random variables related to representations of the braid group B¿. It provides an extension of exchangeability which is tied to the ...

This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows to derive factorization properties from symmetries. ...

Inspired by Lehner's results on exchangeability systems in [Leh06] we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. ...