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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| Huvudupphovsman: | |
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| Materialtyp: | Livre papier |
| Språk: | Anglais |
| Publicerad: |
Princeton (N. J.) ; Oxford :
Princeton University Press
cop. 2010.
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| Serie: | London Mathematical Society monographs series
Vol. 34 |
| Ämnen: | |
| Autres localisations: | Voir dans le Sudoc |
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| 009 | PPN147037425 | ||
| 020 | |a 9780691128290 (rel.) | ||
| 020 | |a 0691128294 (rel.) | ||
| 024 | |a 9780691128290 | ||
| 041 | 0 | |a eng | |
| 082 | |a 519.2 | ||
| 084 | |a 82-02. 2010 | ||
| 084 | |a 33C45. 2010 | ||
| 084 | |a 68B20. 2010 | ||
| 100 | 1 | |a Forrester, Peter. | |
| 245 | 1 | 0 | |a Log-gases and random matrices |c P. J. Forrester. |
| 260 | |a Princeton (N. J.) ; |a Oxford : |b Princeton University Press, |c cop. 2010. | ||
| 300 | |a 1 vol. (XIV-791 p.) : |b couv. ill. en coul. ; |c 26 cm. | ||
| 490 | 1 | |a London Mathematical Society monographs series |v Vol. 34 | |
| 504 | |a Bibliogr. p. [765]-784. Index | ||
| 505 | |a Contient des exercices | ||
| 505 | 0 | |a 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 | |
| 520 | |a "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 polynomials. Peter Forrester presents an encyclopedic developche ment of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multiple of Jacobians ; determinantal point processes and orthogonal polynomials of one variable ; the Selberg integral, Jack polynomials, and generalized hypergeometric functions ; Painlevé transcendents ; macroscopic electrostatistics and asymptotic formuls ; nonintersecting paths and models in statistical mechanisms ; and applications of random matrix theory. This is the first textbook development of both non-symmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles." (source : 4ème de couverture) | ||
| 650 | |a Jacobi, Polynômes de | ||
| 650 | |a Matrices aléatoires | ||
| 650 | |a Intégrales | ||
| 997 | |0 560291 |1 Livre papier |a Ressource papier |c 0/Orléans/ |c 1/Orléans/IDP/ |z Orléans, IDP, 7607 FOR | ||