Random matrices high dimensional phenomena
This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups...
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| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
2009
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| Series: | London Mathematical Society lecture note series
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| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Metric measure spaces
- Lie groups and matrix ensembles
- Entropy and concentration of measure
- Free entropy and equilibrium
- Convergence to equilibrium
- Gradient flows and functional inequalities
- Young tableaux
- Random point fields and random matrices
- Integrable operators and differential equations
- Fluctuations and the Tracy-Widom distribution
- Limit groups and Gaussian measures
- Hermite polynomials
- From the Ornstein-Uhlenbeck process to the Burgers equation
- Noncommutative probability spaces