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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
Eigenvalue Distribution of Large Random Matrices
Hardcover ISBN:  978-0-8218-5285-9
Product Code:  SURV/171
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1398-9
Product Code:  SURV/171.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-5285-9
eBook: ISBN:  978-1-4704-1398-9
Product Code:  SURV/171.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Eigenvalue Distribution of Large Random Matrices
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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
Hardcover ISBN:  978-0-8218-5285-9
Product Code:  SURV/171
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1398-9
Product Code:  SURV/171.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-5285-9
eBook ISBN:  978-1-4704-1398-9
Product Code:  SURV/171.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1712011; 632 pp
    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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1712011; 632 pp
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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