On Bi-R-Diagonal Pairs of Operators

2019/02/04 by Georgios Katsimpas, Katsimpas, Georgios · 1 citation
Mathematics · #46L53 #46L54 #Advanced Algebra and Geometry #FOS: Mathematics #Operator Algebras (math.OA) #Point processes and geometric inequalities #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1902.01041

openalex publication_date 2019/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the properties of the analogue of R-diagonal operators in the setting of bi-free probability. Products of bi-R-diagonal pairs of operators that are *-bi-free are studied and powers of such pairs are found to also be bi-R-diagonal. It is moreover shown that the joint *-distribution of a bi-R-diagonal pair of operators remains invariant under the multiplication by a *-bi-free bi-Haar unitary pair and equivalent characterizations of bi-R-diagonal pairs are developed.

Cited by

• Limit Theorems and Wrapping Transforms in Bi-free Probability Theory

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