Alexandru Nica (Ontario University of Waterloo), Roland Speicher (Ontario Queen's University)

Lectures on the Combinatorics of Free Probability

• Broschiertes Buch

Produktbeschreibung

This 2006 book gives a self-contained and comprehensive introduction to free probability theory and has its main focus on the combinatorial aspects. It can be used as a textbook for an introductory graduate level course, and is also well-suited for the individual study of free probability.

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Produktdetails

• London Mathematical Society Lecture Note Series
• Verlag: Cambridge University Press
• Seitenzahl: 434
• Erscheinungstermin: 15. Oktober 2012
• Englisch
• Abmessung: 229mm x 152mm x 25mm
• Gewicht: 648g
• ISBN-13: 9780521858526
• ISBN-10: 0521858526
• Artikelnr.: 20994686

Autorenporträt

Alexandru Nica is a Professor of Mathematics at the University of Waterloo, Ontario.

Inhaltsangabe

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: 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. 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.