說明 
1 online resource (xv, 417 pages) : digital, PDF file(s) 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 

text file PDF rda 
系列 
London Mathematical Society lecture note series ; 335 

London Mathematical Society lecture note series ; 335

附註 
Title from publisher's bibliographic system (viewed on 05 Oct 2015) 

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: 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. 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 

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 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 
主題 
Free probability theory


Combinatorial analysis

Alt Author 
Speicher, Roland, 1960 author

