Matricial circular systems and random matrices

Abstract

We introduce and study matricial circular systems of operators which play the role of matricial counterparts of circular operators. They describe the asymptotic joint *-distributions of blocks of independent block-identically distributed Gaussian random matrices with respect to partial traces. Using these operators, we introduce circular free Meixner distributions as the non-Hermitian counterparts of free Meixner distributions and construct for them a random matrix model. Our approach is based on the concept of matricial freeness applied to operators on Hilbert spaces. It is closely related to freeness with amalgamation over the algebra [Formula: see text] of [Formula: see text] diagonal matrices applied to operators on Hilbert [Formula: see text]-bimodules.