Matricial circular systems and random matrices

Author:

Lenczewski Romuald1

Affiliation:

1. Wydział Matematyki, Politechnika Wrocławska, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

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.

Funder

Narodowe Centrum Nauki

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory

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