**Mathematical Surveys and Monographs**

Volume: 171;
2011;
632 pp;
Hardcover

MSC: Primary 60; 15;

Print ISBN: 978-0-8218-5285-9

Product Code: SURV/171

List Price: $110.00

Individual Member Price: $88.00

**Electronic ISBN: 978-1-4704-1398-9
Product Code: SURV/171.E**

List Price: $110.00

Individual Member Price: $88.00

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#### Supplemental Materials

# Eigenvalue Distribution of Large Random Matrices

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*Leonid Pastur; Mariya Shcherbina*

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.

#### Table of Contents

# Table of Contents

## Eigenvalue Distribution of Large Random Matrices

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- Introduction 116 free
- Part I. Classical ensembles 3348 free
- Gaussian Ensembles: Semicircle law 3550
- Gaussian Ensembles: Central Limit Theorem for linear eigenvalue statistics 6984
- Gaussian Ensembles: Joint eigenvalue distribution and related results 101116
- Gaussian Unitary Ensemble 129144
- Gaussian Orthogonal Ensemble 159174
- Wishart and Laguerre Ensembles 177192
- Classical compact groups ensembles: Global regime 211226
- Classical compact group ensembles: Local regime 249264
- Law of addition of random matrices 275290
- Part II. Matrix Models 315330
- Matrix Models: Global regime 317332
- Bulk universality for hermitian Matrix Models 369384
- Universality for special points of hermitian Matrix Models 385400
- Jacobi matrices and limiting laws for linear eigenvalue statistics 437452
- Universality for real symmetric Matrix Models 469484
- Unitary Matrix Models 485500
- Part III. Ensembles with independent and weakly dependent entries 499514
- Matrices with Gaussian correlated entries 501516
- Wigner Ensembles 525540
- Sample covariance and related matrices 583598
- Bibliography 611626
- Index 631646 free
- Back Cover Back Cover1650

#### Readership

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

#### 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