Journal article
Free random variables whose free distributions are dictated by the semicircular law
Advances in operator theory, Vol.9(2), 34
2024
DOI: 10.1007/s43036-024-00334-9
Abstract
In this paper, we study free-probabilistic structures of C∗-algebras generated by mutually free, multi free random variables followed by the semicircular law in a certain sense. Our main results (i) show that a semicircular element in a C∗-probability space A,φ, and a certain ∗-isomorphism on A generate countable-infinitely many free random variables followed by the semicircular law, (ii) illustrate that, from mutually free, multi free random variables of (i), the corresponding C∗-probability spaces are well-determined, and (iii) characterize not only free-probabilistic structures, but also free-distributional data on the C∗-probability spaces of (ii). As application, we study some types of free random variables followed by the circular law, and followed by free Poisson distributions in certain senses.
Details
- Title: Subtitle
- Free random variables whose free distributions are dictated by the semicircular law
- Creators
- Ilwoo Cho - Saint Ambrose UniversityPalle E. T. Jorgensen - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Advances in operator theory, Vol.9(2), 34
- Publisher
- Springer International Publishing
- DOI
- 10.1007/s43036-024-00334-9
- ISSN
- 2662-2009
- eISSN
- 2538-225X
- Language
- English
- Date published
- 2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984582434102771
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