Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence

Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence
Author :
Publisher : American Mathematical Society
Total Pages : 100
Release :
ISBN-10 : 9781470442989
ISBN-13 : 1470442981
Rating : 4/5 (981 Downloads)

Book Synopsis Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence by : Camille Male

Download or read book Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence written by Camille Male and published by American Mathematical Society. This book was released on 2021-02-10 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.


Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence Related Books

Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence
Language: en
Pages: 100
Authors: Camille Male
Categories: Mathematics
Type: BOOK - Published: 2021-02-10 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion
Random Matrices and Non-Commutative Probability
Language: en
Pages: 420
Authors: Arup Bose
Categories: Mathematics
Type: BOOK - Published: 2021-10-26 - Publisher: CRC Press

DOWNLOAD EBOOK

This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are in
The Yang-Mills Heat Equation with Finite Action in Three Dimensions
Language: en
Pages: 111
Authors: Leonard Gross
Categories: Mathematics
Type: BOOK - Published: 2022-02-02 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

View the abstract.
Infinity Operads And Monoidal Categories With Group Equivariance
Language: en
Pages: 486
Authors: Donald Yau
Categories: Mathematics
Type: BOOK - Published: 2021-12-02 - Publisher: World Scientific

DOWNLOAD EBOOK

This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action
Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
Language: en
Pages: 100
Authors: William Gignac
Categories: Mathematics
Type: BOOK - Published: 2021-11-16 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

View the abstract.