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Eigenvalue Distribution of Large Random Matrices
About this Title
Leonid Pastur, Ukrainian National Academy of Sciences, Kharkov, Ukraine and Mariya Shcherbina, Ukrainian National Academy of Sciences, Kharkov, Ukraine
Publication: Mathematical Surveys and Monographs
Publication Year:
2011; Volume 171
ISBNs: 978-0-8218-5285-9 (print); 978-1-4704-1398-9 (online)
DOI: https://doi.org/10.1090/surv/171
MathSciNet review: 2808038
MSC: Primary 60B20; Secondary 15A18, 15B52, 60F05, 62H10, 62H99
Table of Contents
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Front/Back Matter
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