Fluctuation Moments Induced by Conjugation with Asymptotically Liberating Random Matrix Ensembles

Josue Vazquez-Becerra ()
Additional contact information
Josue Vazquez-Becerra: Queen’s University

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 1972-2039

Abstract: Abstract Independent Haar-unitary random matrices and independent Haar-orthogonal random matrices are known to be asymptotically liberating ensembles, and they give rise to asymptotic free independence when used for conjugation of constant matrices. G. Anderson and B. Farrel showed that a certain family of discrete random unitary matrices can actually be used to the same end. In this paper, we investigate fluctuation moments and higher-order moments induced on constant matrices by conjugation with asymptotically liberating ensembles. We show for the first time that the fluctuation moments associated with second-order free independence can be obtained from conjugation with an ensemble consisting of signed permutation matrices and the discrete Fourier transform matrix. We also determine fluctuation moments induced by various related ensembles where we do not get known expressions but others related to traffic free independence.

Keywords: Free probability; Random matrices; Fluctuation moments; Discrete Fourier transform matrix; 46I54; 60B20; 15B52 (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-023-01246-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01246-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-023-01246-9

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().