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Cover: 9781493969418 | Free Probability and Random Matrices | Roland Speicher (u. a.) | Buch
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Free Probability and Random Matrices
Buch von Roland Speicher (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

Covers a variety of different facets of free probability, giving a flavor of the breadth of the subject

Features exercises scattered throughout the text

Showcases basic ideas and results in order to focus on their relation

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2017
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xiv
336 S.
45 s/w Illustr.
336 p. 45 illus.
ISBN-13: 9781493969418
ISBN-10: 1493969412
Sprache: Englisch
Einband: Gebunden
Autor: Speicher, Roland
Mingo, James A.
Auflage: 1st edition 2017
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 25 mm
Von/Mit: Roland Speicher (u. a.)
Erscheinungsdatum: 26.06.2017
Gewicht: 0,694 kg
Artikel-ID: 109473589
Zusammenfassung

Covers a variety of different facets of free probability, giving a flavor of the breadth of the subject

Features exercises scattered throughout the text

Showcases basic ideas and results in order to focus on their relation

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2017
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xiv
336 S.
45 s/w Illustr.
336 p. 45 illus.
ISBN-13: 9781493969418
ISBN-10: 1493969412
Sprache: Englisch
Einband: Gebunden
Autor: Speicher, Roland
Mingo, James A.
Auflage: 1st edition 2017
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 25 mm
Von/Mit: Roland Speicher (u. a.)
Erscheinungsdatum: 26.06.2017
Gewicht: 0,694 kg
Artikel-ID: 109473589
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