Book chapter
Vertex-Glued Connected Finite Graphs and Mutually Free Semicircular Elements
Schur Analysis and Applications to Hypercomplex Analysis, Neural Networks, and Linear Systems, pp.203-243
Operator Theory: Advances and Applications, Springer Nature Switzerland
2026
DOI: 10.1007/978-3-032-02315-5_7
Abstract
In this chapter, we study a certain type of C∗ C^(*) -probability spaces induced by connected finite directed graphs. We are interested in free product of such C∗ C^(*) -probability spaces obtained by a combinatorial process constructing new graphs from given multigraphs under a rule, called the gluing. We characterize operator-algebraic, and free-probabilistic structures of resulted C∗ C^(*) -probability spaces from the gluing in terms of (free-probability-theoretic) free product (also implying the combinatorial properties of graphs), and consider free-distributional data on them. In particular, we are interested in semicircular elements whose free distributions are the semicircular law.
Details
- Title: Subtitle
- Vertex-Glued Connected Finite Graphs and Mutually Free Semicircular Elements
- Creators
- Ilwoo Cho - Saint Ambrose UniversityPalle E. T. Jorgensen - University of Iowa
- Contributors
- Daniel Alpay (Editor)Izchak Lewkowicz (Editor)Adrian Vajiac (Editor)Mihaela Vajiac (Editor)
- Resource Type
- Book chapter
- Publication Details
- Schur Analysis and Applications to Hypercomplex Analysis, Neural Networks, and Linear Systems, pp.203-243
- Series
- Operator Theory: Advances and Applications
- DOI
- 10.1007/978-3-032-02315-5_7
- eISSN
- 2296-4878
- ISSN
- 0255-0156
- Publisher
- Springer Nature Switzerland; Cham
- Language
- English
- Date published
- 2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985163544102771
Metrics
1 Record Views