The semicircular law of free probability as noncommutative multivariable operator theory

被引：0
作者：
Ilwoo Cho
Palle E. T. Jorgensen
机构：
[1] St. Ambrose University,Department of Mathematics and Statistics
[2] The University of Iowa,Department of Mathematics
来源：
Advances in Operator Theory | 2021年 / 6卷
关键词：
Graphs; Graph groupoids; Semicircular elements; The semicircular law; 47A99; 05C62; 17A50; 18B40;
D O I：
暂无
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学科分类号：
摘要：
In this paper, we study semicircular elements induced by connected finite directed graphs. It is shown that if the graph groupoid G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {G}$$\end{document} of a given graph G contains at least one loop finite path, then it induces a semicircular element under suitable representations of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {G}$$\end{document}. As application, if a graph G is fractal (or, satisfies the fractal property) in a certain sense, then it automatically generates infinitely many semicircular elements.
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