An introduction to the behaviour of random matrices. Suitable for postgraduate students and non-experts.

Gordon Blower is currently Head of the Department of Mathematics and Statistics at Lancaster University, and Professor of Mathematical Analysis.

Introduction; 1. Metric Measure spaces; 2. Lie groups and matrix ensembles; 3. Entropy and concentration of measure; 4. Free entropy and equilibrium; 5. Convergence to equilibrium; 6. Gradient ows and functional inequalities; 7. Young tableaux; 8. Random point fields and random matrices; 9. Integrable operators and differential equations; 10. Fluctuations and the Tracy-Widom distribution; 11. Limit groups and Gaussian measures; 12. Hermite polynomials; 13. From the Ornstein-Uhlenbeck process to Burger's equation; 14. Noncommutative probability spaces; References; Index.