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Free probability and random matrices [electronic resource]

Free probability and random matrices [electronic resource]

Material type
E-Book(소장)
Personal Author
Mingo, James A. Speicher, Roland.
Title Statement
Free probability and random matrices [electronic resource] / James A. Mingo, Roland Speicher.
Publication, Distribution, etc
New York :   Springer,   c2017.  
Physical Medium
1 online resource (xiv, 336 p.) : ill.
Series Statement
Fields Institute Monographs,1069-5273 ; 35
ISBN
9781493969418 9781493969425 (e-book)
요약
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
General Note
Title from e-Book title page.  
Content Notes
1. Asymptotic Freeness of Gaussian Random Matrices -- 2. The Free Central Limit Theorem and Free Cumulants -- 3. Free Harmonic Analysis -- 4. Asymptotic Freeness -- 5. Second Order Freeness -- 6. Free Group Factors and Freeness -- 7. Free Entropy X-the Microstates Approach via Large Deviations -- Free Entropy X*-the Non-Microstates Approach via Free Fisher Information -- 9. Operator-Valued Free Probability Theory and Block Random Matrices -- 10. Polynomials in Free Variables and Operator-Valued Convolution -- 11. Brown Measure -- Solutions to Exercises -- References -- Index of Exercises.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Free probability theory. Random matrices. Functional analysis.
Short cut
URL
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020 ▼a 9781493969418
020 ▼a 9781493969425 (e-book)
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050 0 0 ▼a QA326
082 0 4 ▼a 512.55 ▼2 22
084 ▼a 512.55 ▼2 DDCK
090 ▼a 512.55
100 1 ▼a Mingo, James A.
245 1 0 ▼a Free probability and random matrices ▼h [electronic resource] / ▼c James A. Mingo, Roland Speicher.
260 ▼a New York : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (xiv, 336 p.) : ▼b ill.
490 1 ▼a Fields Institute Monographs, ▼x 1069-5273 ; ▼v 35
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a 1. Asymptotic Freeness of Gaussian Random Matrices -- 2. The Free Central Limit Theorem and Free Cumulants -- 3. Free Harmonic Analysis -- 4. Asymptotic Freeness -- 5. Second Order Freeness -- 6. Free Group Factors and Freeness -- 7. Free Entropy X-the Microstates Approach via Large Deviations -- Free Entropy X*-the Non-Microstates Approach via Free Fisher Information -- 9. Operator-Valued Free Probability Theory and Block Random Matrices -- 10. Polynomials in Free Variables and Operator-Valued Convolution -- 11. Brown Measure -- Solutions to Exercises -- References -- Index of Exercises.
520 ▼a This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Free probability theory.
650 0 ▼a Random matrices.
650 0 ▼a Functional analysis.
700 1 ▼a Speicher, Roland.
830 0 ▼a Fields Institute Monographs; ▼v 35.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-1-4939-6942-5
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.55 Accession No. E14016758 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

1. Asymptotic Freeness of Gaussian Random Matrices.- 2. The Free Central Limit Theorem and Free Cumulants.- 3. Free Harmonic Analysis.- 4. Asymptotic Freeness.- 5. Second Order Freeness.- 6. Free Group Factors and Freeness.- 7. Free Entropy X-the Microstates Approach via Large Deviations.- Free Entropy X -the Non-Microstates Approach via Free Fisher Information.- 9. Operator-Valued Free Probability Theory and Block Random Matrices.- 10. Polynomials in Free Variables and Operator-Valued Convolution.- 11. Brown Measure.- Solutions to Exercises.- References.- Index of Exercises.


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