2011/01/04 by Curran, Stephen, Speicher, Roland
#46L54 (46L65 #60G09) #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)
paper · doi:10.48550/arxiv.1101.0795
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.