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Eigenvalue Distribution of Large Random Matrices

Leonid Pastur Ukrainian National Academy of Sciences, Kharkov, Ukraine
Mariya Shcherbina Ukrainian National Academy of Sciences, Kharkov, Ukraine
Available Formats:
Hardcover ISBN: 978-0-8218-5285-9
Product Code: SURV/171
632 pp
List Price: $117.00 MAA Member Price:$105.30
AMS Member Price: $93.60 Electronic ISBN: 978-1-4704-1398-9 Product Code: SURV/171.E 632 pp List Price:$110.00
MAA Member Price: $99.00 AMS Member Price:$88.00
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List Price: $175.50 MAA Member Price:$157.95
AMS Member Price: $140.40 Click above image for expanded view Eigenvalue Distribution of Large Random Matrices Leonid Pastur Ukrainian National Academy of Sciences, Kharkov, Ukraine Mariya Shcherbina Ukrainian National Academy of Sciences, Kharkov, Ukraine Available Formats:  Hardcover ISBN: 978-0-8218-5285-9 Product Code: SURV/171 632 pp  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$93.60
 Electronic ISBN: 978-1-4704-1398-9 Product Code: SURV/171.E 632 pp
 List Price: $110.00 MAA Member Price:$99.00 AMS Member Price: $88.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$175.50
MAA Member Price: $157.95 AMS Member Price:$140.40
• Book Details

Mathematical Surveys and Monographs
Volume: 1712011
MSC: Primary 60; 15;

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries).

The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes.

This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.

Graduate students and research mathematicians interested in random matrix theory and its applications.

• Chapters
• 1. Introduction
• Part 1. Classical ensembles
• 2. Gaussian ensembles: Semicircle law
• 3. Gaussian ensembles: Central Limit Theorem for linear eigenvalue statistics
• 4. Gaussian ensembles: Joint eigenvalue distribution and related results
• 5. Gaussian unitary ensemble
• 6. Gaussian orthogonal ensemble
• 7. Wishart and Laguerre ensembles
• 8. Classical compact groups ensembles: Global regime
• 9. Classical compact group ensembles: Further results
• 10. Law of addition of random matrices
• Part 2. Matrix models
• 11. Matrix models: Global regime
• 12. Bulk universality for Hermitian matrix models
• 13. Universality for special points of Hermitian matrix models
• 14. Jacobi matrices and limiting laws for linear eigenvalue statistics
• 15. Universality for real symmetric matrix models
• 16. Unitary matrix models
• Part 3. Ensembles with independent and weakly dependent entries
• 17. Matrices with Gaussian correlated entries
• 18. Wigner ensembles
• 19. Sample covariance and related matrices

• Reviews

• While a wide variety of ensembles are studied in this text, the methods are coherently focused, relying heavily in particular on Stieltjes transform based tools. This gives a slightly different perspective on the subject from other recent texts which often focus on other methods.

Mathematical Reviews
• Request Review Copy
• Get Permissions
Volume: 1712011
MSC: Primary 60; 15;

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries).

The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes.

This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.

Graduate students and research mathematicians interested in random matrix theory and its applications.

• Chapters
• 1. Introduction
• Part 1. Classical ensembles
• 2. Gaussian ensembles: Semicircle law
• 3. Gaussian ensembles: Central Limit Theorem for linear eigenvalue statistics
• 4. Gaussian ensembles: Joint eigenvalue distribution and related results
• 5. Gaussian unitary ensemble
• 6. Gaussian orthogonal ensemble
• 7. Wishart and Laguerre ensembles
• 8. Classical compact groups ensembles: Global regime
• 9. Classical compact group ensembles: Further results
• 10. Law of addition of random matrices
• Part 2. Matrix models
• 11. Matrix models: Global regime
• 12. Bulk universality for Hermitian matrix models
• 13. Universality for special points of Hermitian matrix models
• 14. Jacobi matrices and limiting laws for linear eigenvalue statistics
• 15. Universality for real symmetric matrix models
• 16. Unitary matrix models
• Part 3. Ensembles with independent and weakly dependent entries
• 17. Matrices with Gaussian correlated entries
• 18. Wigner ensembles
• 19. Sample covariance and related matrices
• While a wide variety of ensembles are studied in this text, the methods are coherently focused, relying heavily in particular on Stieltjes transform based tools. This gives a slightly different perspective on the subject from other recent texts which often focus on other methods.

Mathematical Reviews
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