Quantum invariant families of matrices in free probability
Operator Algebras
2011-01-05 v1 Probability
Abstract
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 -cyclicity condition. This is a surprising contrast with the Aldous-Hoover characterization of jointly exchangeable arrays.
Keywords
Cite
@article{arxiv.1101.0795,
title = {Quantum invariant families of matrices in free probability},
author = {Stephen Curran and Roland Speicher},
journal= {arXiv preprint arXiv:1101.0795},
year = {2011}
}
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33 pages