Log-gases and random matrices

Log-gases and random matrices

"Random matrix theory, both as an application and as theory, has evolved rapidly over the past fifteen years. [This book] gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack po...

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Détails bibliographiques
Auteur principal : Forrester Peter (Auteur)
Format : Livre
Langue : anglais
Titre complet : Log-gases and random matrices / P. J. Forrester
Publié : Princeton (N. J.), Oxford : Princeton University Press , cop. 2010
Description matérielle : 1 vol. (XIV-791 p.)
Collection : London Mathematical Society monographs series editors Martin Bridson, Terry Lyons, Peter Sarnak,... ; 34
Contenu : Contient des exercices
Sujets :
Jacobi, Polynômes de
Matrices aléatoires
Intégrales
  • Chapter 1. Gaussian matrix ensembles
  • Chapter 2. Circular ensembles
  • Chapter 3. Laguerre and Jacobi ensembles
  • Chapter 4. The Selberg integral
  • Chapter 5. Correlation functions at [beta ]=2
  • Chapter 6. Correlation functions at [beta]=1 and 4
  • Chapter 7. Scaled limits at [beta]=1, 2 and 4
  • Chapter 8. Eigenvalue probabilities - Painlevé systems approach
  • Chapter 9. Eigenvalue probabilities - Fredholm determinant approach
  • Chapter 10. Lattice paths and growth models
  • Chapter 11. The Calogero-Sutherland model
  • Chapter 12. Jack polynomials
  • Chapter 13. Correlations for general [beta]
  • Chapter 14. Fluctuations formulas and universal behavior of correlations
  • Chapter 15. The two-dimensional one-component plasma