Lectures on the Combinatorics of Free Probability

ISBN: 9780521858526 出版年：2006 页码：435 Alexandru Nica Roland Speicher Cambridge University Press

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: Mobius 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.