Topic
Free convolution
About: Free convolution is a research topic. Over the lifetime, 204 publications have been published within this topic receiving 8910 citations.
Papers published on a yearly basis
Papers
Book•
11 Sep 2006TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.
Abstract: 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.
1,450 citations
TL;DR: In this paper, it was shown that free random variables naturally arise as limits of random matrices and that Wigner's semicircle law is a consequence of the central limit theorem for free variables.
Abstract: In earlier articles we studied a kind of probability theory in the framework of operator algebras, with the tensor product replaced by the free product. We prove here that free random variables naturally arise as limits of random matrices and that Wigner's semicircle law is a consequence of the central limit theorem for free random variables. In this way we obtain a non-commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra, Wigner's law being given by the trace of the spectral measure of the selfadjoint component of this operator
982 citations
1 Jan 1985
757 citations
Book•
1 Jan 2000TL;DR: In this paper, the free relation between probability laws and non-commutative random variables has been studied in the context of analytic function theory and infinitely divisible laws for random matrices and asymptotically free relation.
Abstract: Overview Probability laws and noncommutative random variables The free relation Analytic function theory and infinitely divisible laws Random matrices and asymptotically free relation Large deviations for random matrices Free entropy of noncommutative random variables Relation to operator algebras Bibliography Index.
652 citations
Book•
1 Jun 1998
TL;DR: In this paper, the lattice of non-crossing partitions has been studied in the context of operator-valued multiplicative functions on the lattices of noncrossing partition.
Abstract: Preliminaries on non-crossing partitions Operator-valued multiplicative functions on the lattice of non-crossing partitions Amalgamated free products Operator-valued free probability theory Operator-valued stochastic processes and stochastic differential equations Bibliography.
551 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 8 |
| 2020 | 10 |
| 2019 | 6 |
| 2018 | 10 |
| 2017 | 9 |