Free Probability and Operator Algebras [electronic resource] /
Dan-Virgil Voiculescu, Nicolai Stammeier, Moritz Weber
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2016
- 1 online resource (142 pages)
- Münster Lectures in Mathematics (MLM) .
Background and outlook / Basics in free probability / Random matrices and combinatorics / Free monotone transport / Free group factors / Free convolution / Easy quantum groups / Dan-Virgil Voiculescu -- Moritz Weber -- Roland Speicher -- Dimitri L. Shlyakhtenko -- Ken Dykema -- Hari Bercovici -- Moritz Weber.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
Free probability is a probability theory dealing with variables having the highest degree of noncommutativity, an aspect found in many areas (quantum mechanics, free group algebras, random matrices etc). Thirty years after its foundation, it is a well-established and very active field of mathematics. Originating from Voiculescu’s attempt to solve the free group factor problem in operator algebras, free probability has important connections with random matrix theory, combinatorics, harmonic analysis, representation theory of large groups, and wireless communication. These lecture notes arose from a masterclass in Münster, Germany and present the state of free probability from an operator algebraic perspective. This volume includes introductory lectures on random matrices and combinatorics of free probability (Speicher), free monotone transport (Shlyakhtenko), free group factors (Dykema), free convolution (Bercovici), easy quantum groups (Weber), and a historical review with an outlook (Voiculescu). In order to make it more accessible, the exposition features a chapter on basics in free probability, and exercises for each part. This book is aimed at master students to early career researchers familiar with basic notions and concepts from operator algebras.
9783037196656
10.4171/165 doi
Functional analysis
Groups & group theory
Functional analysis
Group theory and generalizations
Operator theory
Probability theory and stochastic processes
Background and outlook / Basics in free probability / Random matrices and combinatorics / Free monotone transport / Free group factors / Free convolution / Easy quantum groups / Dan-Virgil Voiculescu -- Moritz Weber -- Roland Speicher -- Dimitri L. Shlyakhtenko -- Ken Dykema -- Hari Bercovici -- Moritz Weber.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
Free probability is a probability theory dealing with variables having the highest degree of noncommutativity, an aspect found in many areas (quantum mechanics, free group algebras, random matrices etc). Thirty years after its foundation, it is a well-established and very active field of mathematics. Originating from Voiculescu’s attempt to solve the free group factor problem in operator algebras, free probability has important connections with random matrix theory, combinatorics, harmonic analysis, representation theory of large groups, and wireless communication. These lecture notes arose from a masterclass in Münster, Germany and present the state of free probability from an operator algebraic perspective. This volume includes introductory lectures on random matrices and combinatorics of free probability (Speicher), free monotone transport (Shlyakhtenko), free group factors (Dykema), free convolution (Bercovici), easy quantum groups (Weber), and a historical review with an outlook (Voiculescu). In order to make it more accessible, the exposition features a chapter on basics in free probability, and exercises for each part. This book is aimed at master students to early career researchers familiar with basic notions and concepts from operator algebras.
9783037196656
10.4171/165 doi
Functional analysis
Groups & group theory
Functional analysis
Group theory and generalizations
Operator theory
Probability theory and stochastic processes