Quantum invariant families of matrices in free probability

Details Quantum invariant families of matrices in free probability Quantum invariant families of matrices in free probability

2011-01-04

arxiv.org/abs/1101.0795v1

Mathematics

Operator Algebras

33 pages

Scientific paper

We consider (self-adjoint) families of infinite matrices of noncommutative random variables such that the joint distribution of their entries is invariant under conjugation by a free quantum group. For the free orthogonal and hyperoctahedral groups, we obtain complete characterizations of the invariant families in terms of an operator-valued $R$-cyclicity condition. This is a surprising contrast with the Aldous-Hoover characterization of jointly exchangeable arrays.

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