Bibliogr. p. 655-679. Index

Chapter 1. Introduction Chapter 2. Gaussian ensembles. The joint probability density function for the matrix elements Chapter 3. Gaussian ensembles. The joint probability density function for the eigenvalues Chapter 4. Gaussian ensembles level density Chapter 5. Orthogonal, skew-orthogonal and bi-orthogonal polynomials Chapter 6. Gaussian unitary ensemble Chapter 7. Gaussian orthogonal ensemble Chapter 8. Gaussian symplectic ensemble Chapter 9. Gaussian ensembles : brownian motion model Chapter 10. Circular ensembles Chapter 11. Circular ensembles (continued) Chapter 12. Circular ensembles. Thermodynamics Chapter 13. Gaussian ensemble of anti-symmetric hermitian matrices Chapter 14. a gaussian ensemble for hermitian matrices with unequal real and imaginary parts Chapter 15. Matrices with gaussian element desnsities but with non unitary or hermitian conditions imposed Chapter 16. Statistical analysis of a level-sequence Chapter 17. Selberg's integral and its consequences Chapter 18. Asymptotic behaviour of Eβ(0,s) by inverse scattering Chapter 19. Matrix ensembles and classical orthogonal polynomials Chapter 20. Level spacing functions Eβ(r,s) : inter-relations and power series expansions Chapter 21. Fredholm determinants and Painlevé equations Chapter 22. Moments of the characteristics polynomila in the three ensembles of random matrices Chapter 23. Hermitian matrices coupled in a chain Chapter 24. Gaussian ensembles. Edge of the spectrum Chapter 25. Random permutations, circular unitary ensemble (CUE) and gaussian unitary ensemble (GUE) Chapter 26. Probability densities of the determinants ; Gaussian ensembles Chapter 27. Restrited trace ensembles Appendices