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 A of r x r diagonal matrices applied to operators on Hilbert A-bimodules.
Cite
@article{arxiv.1311.6420,
title = {Matricial circular systems and random matrices},
author = {Romuald Lenczewski},
journal= {arXiv preprint arXiv:1311.6420},
year = {2018}
}
Comments
27 pages, major revision, results on the relation to operator-valued free probability are new