Lectures on the Combinatorics of Free Probability
1st Edition
Published on 22. March 2011
978-0-511-89389-6 (ISBN)
Description
Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.
Reviews / Votes
"This book is an absolutely indispensable resource for anyone who works in free probability theory, as well as those (advanced undergraduates or graduate students, or professional researchers) newly initiated in the field. Lectures on the Combinatorics of Free Probabilityis sure to be considered one of the important informative texts in this rapidly growing field of study, and it is highly recommended for any reader or researcher in the field."Todd Kemp, Mathematical Reviews
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 124 Tables, color
File size
7,92 MB
ISBN-13
978-0-511-89389-6 (9780511893896)
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Schweitzer Classification
Other editions
Additional editions
Alexandru Nica | Roland Speicher
Lectures on the Combinatorics of Free Probability
Book
09/2006
Cambridge University Press
€144.60
Shipment within 15-20 days
Persons
Alexandru Nica is a Professor of Mathematics at the University of Waterloo, Ontario. Roland Speicher is a Professor of Mathematics at Queen's University, Kingston.
Content
Part I. Basic Concepts: 1. Non-commutative probability spaces and distributions; 2. A case study of non-normal distribution; 3. C*-probability spaces; 4. Non-commutative joint distributions; 5. Definition and basic properties of free independence; 6. Free product of *-probability spaces; 7. Free product of C*-probability spaces; Part II. Cumulants: 8. Motivation: free central limit theorem; 9. Basic combinatorics I: non-crossing partitions; 10. Basic Combinatorics II: Moebius inversion; 11. Free cumulants: definition and basic properties; 12. Sums of free random variables; 13. More about limit theorems and infinitely divisible distributions; 14. Products of free random variables; 15. R-diagonal elements; Part III. Transforms and Models: 16. The R-transform; 17. The operation of boxed convolution; 18. More on the 1-dimensional boxed convolution; 19. The free commutator; 20. R-cyclic matrices; 21. The full Fock space model for the R-transform; 22. Gaussian Random Matrices; 23. Unitary Random Matrices; Notes and Comments; Bibliography; Index.
