Free Random Variables

Free Distributions Dictated by the Semicircular Law

Ilwoo Cho (Saint Ambrose University, Iowa)

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English

CRC Press
13 November 2025

Complex analysis, complex variables; Probability & statistics; Computing: general; Computer science

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Free Random Variables: Free Distributions Dictated by the Semicircular Law is particularly concerned with operators which are not self-adjoint, but whose free distributions are dictated by the semicircular law. The book covers operator-theoretic properties and free-distributional data of such operators and investigates operator-algebraic structures induced by those operators.

Features

Includes multiple examples and applications Suitable for postgraduates and researchers

By: Ilwoo Cho (Saint Ambrose University Iowa)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9781041103462
ISBN 10: 1041103468
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 124
Publication Date: 13 November 2025
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

I Constructive Analysis of Free Random Variables Followed by the Semicircular Law 1 Introduction 2 Preliminaries 3 Free Distributions of Multi Semicircular Elements 4 A C∗-Probability Space Generated by |N|-Many Semicircular Elements 5 Free-Distributional Data on Xϕ 6 Certain Free-Isomorphisms on Xϕ 7 Free Random Variables followed by the Semicircular Law 8 Free Random Variables Followed by the Circular Law 9 Free Random Variables Followed by Free Poisson Distributions 10 Discussions 11 A Structure Theorem of Xτ 12 Certain Banach-Space Operators Acting on Xτ 13 A Group-Dynamical System (Z, Xτ , α) 14 More About Free-Distributional Data on X [Γ] II Free Random Variables followed by the Semicircular Law 15 Free Random Variables Followed By The Semicircular Law 16 On the Copies of the C∗-Probability Space Xτ 17 Finitely-Many Free Random Variables Governed by The Semicircular Law 18 Generalization 19 Applications Bibliography

Ilwoo Cho is a Professor at St. Ambrose University in the Department of Mathematics and Statistics, USA. He completed his Ph.D from the University of Iowa, Department of Mathematics, in 2005. His research interests are Free Probability, Operator Algebra, Operator Theory, Combinatorics, Dynamical Systems, and Hypercomplex Analysis.