Book chapter
On Semicircular Elements Induced by Connected Finite Graphs
Matrix and Operator Equations and Applications, pp.583-631
Mathematics Online First Collections, Springer Nature Switzerland
01/01/2023
DOI: 10.1007/16618_2023_57
Abstract
In this chapter, we study C∗-probability spaces which are induced by finite graphs. We first introduce classes if graph groupoids (derived from connected graphs). We then show that their representations act on specific C∗-probability spaces. Via these representations, we further show that groupoidal elements will then act as Banach-space operators, realized on our free-probabilistic structures, in such a way that they deform the original free-distributional data. We characterize the deformations arising this way from individual graph-groupoid elements. Applications are given to deformed semicircular laws.
Details
- Title: Subtitle
- On Semicircular Elements Induced by Connected Finite Graphs
- Creators
- Ilwoo Cho - Saint Ambrose UniversityPalle E. T. Jorgensen - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Matrix and Operator Equations and Applications, pp.583-631
- Publisher
- Springer Nature Switzerland; Cham
- Series
- Mathematics Online First Collections
- DOI
- 10.1007/16618_2023_57
- eISSN
- 2730-6348
- ISSN
- 2730-633X
- Language
- English
- Date published
- 01/01/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984449560202771
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