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Lectures on the Combinatorics of Free Probability

Author: Alexandru Nica; Roland Speicher
Publisher: Cambridge : Cambridge University Press, 2006.
Series: London Mathematical Society lecture note series, no. 335.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.
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Additional Physical Format: Version imprimée :
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alexandru Nica; Roland Speicher
ISBN: 9780511735127 051173512X 9780521858526 0521858526 9781107368088 1107368081 9781107363168 1107363160
OCLC Number: 1104455892
Description: 1 ressource en ligne (436 pages).
Contents: 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: M s 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.
Series Title: London Mathematical Society lecture note series, no. 335.
Responsibility: Alexandru Nica, Roland Speicher.

Abstract:

This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

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