Random matrices

Random matrices

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Auteur principal : Mehta Madan Lal (Auteur)
Format : Livre
Langue : anglais
Titre complet : Random matrices / Madan Lal Mehta
Édition : 3rd ed.
Publié : Amsterdam, Boston, Paris [etc.] : Elsevier , cop. 2004
Academic Press
Description matérielle : 1 vol. (XVIII-688 p.)
Collection : Pure and applied mathematics (New York. 1949) ; 142
Sujets :
Matrices aléatoires
Matrices, Mécanique des > Modèles mathématiques
Perturbation (théorie quantique)
Théorie quantique
Niveaux d'énergie (théorie quantique) > Méthodes statistiques
  • 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 Eb(0,s) by inverse scattering
  • Chapter 19. Matrix ensembles and classical orthogonal polynomials
  • Chapter 20. Level spacing functions Eb(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