Lectures on the Combinatorics of Free Probability
$125.99 (C)
Part of London Mathematical Society Lecture Note Series
 Authors:
 Alexandru Nica, University of Waterloo, Ontario
 Roland Speicher, Queen's University, Ontario
 Date Published: September 2006
 availability: Available
 format: Paperback
 isbn: 9780521858526
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125.99
(C)
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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 book is the first to give a selfcontained 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 wellsuited for the individual study of free probability.
Read more Presents the state of the art of the combinatorial facet of free probability
 Gives a friendly and selfcontained introduction to the general field of free probability
 Written in a style which makes it ideal for use in the presentation of a graduate level course
Reviews & endorsements
"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 ReviewsCustomer reviews
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×Product details
 Date Published: September 2006
 format: Paperback
 isbn: 9780521858526
 length: 434 pages
 dimensions: 229 x 152 x 25 mm
 weight: 0.63kg
 contains: 124 exercises
 availability: Available
Table of Contents
Part I. Basic Concepts:
1. Noncommutative probability spaces and distributions
2. A case study of nonnormal distribution
3. C*probability spaces
4. Noncommutative 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: noncrossing partitions
10. Basic Combinatorics II: Möbius 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. Rdiagonal elements
Part III. Transforms and Models:
16. The Rtransform
17. The operation of boxed convolution
18. More on the 1dimensional boxed convolution
19. The free commutator
20. Rcyclic matrices
21. The full Fock space model for the Rtransform
22. Gaussian Random Matrices
23. Unitary Random Matrices
Notes and Comments
Bibliography
Index.
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