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

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. --- summary provided by publisher