Integrals over classical groups, random permutations, toda and toeplitz lattices

Communications on Pure and Applied Mathematics

Volumn 54, Issue 2, 2001, Pages 153-205

  Adler, Mark ^a   Van Moerbeke, Pierre ^a,b  

^a BRANDEIS UNIVERSITY   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035578398     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0312(200102)54:2<153::AID-CPA2>3.0.CO;2-5     Document Type: Article

References (19)

1. Adler, M.;van Moerbeke, P. Matrix integrals, Toda symmetries, Virasoro constraints and orthogonal polynomials. Duke Math. J. 80 (1995), no. 3, 863-911.
2. Adler, M.;van Moerbeke, P. String-orthogonal polynomials, string equations, and 2-Toda symmetries. Comm. Pure and Appl. Math. 50 (1997), no. 3, 241-290.
3. Adler, M.;van Moerbeke, P. The spectrum of coupled random matrices. Ann. of Math. (2) 149 (1999), no. 3, 921-976.
4. Adler, M.;van Moerbeke, P. Vertex operator solutions to the discrete KP-hierarchy. Comm. Math. Phys. 203 (1999), no. 1, 185-210.
5. Aldous, D.; Diaconis, P. Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 4, 413-432.
6. Aomoto, K. Jacobi polynomials associated with Selberg integrals. SIAM J. Math. Anal. 18 (1987), no. 2, 545-549.
7. Baik, J.; Deift, P.; Johansson, K. On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (1999), no. 4, 1119-1178.
8. Baik, J.; Rains, E. Algebraic aspects of increasing subsequences. Preprint Math. CO/9905083 B, 1999.
9. Cosgrove, C. M. Chazy classes IX-XI of third-order differential equations. Stud. Appl. Math. 104 (2000), no. 3, 171-228.
10. Cosgrove, C. M.; Scoufis, G. Painlevé classification of a class of differential equations of the second order and second degree. Stud. Appl. Math. 88 (1993), no. 1, 25-87.
11. Diaconis, P.; Shahshahani, M. On the eigenvalues of random matrices. Studies in applied probability. J. Appl. Probab. 31A (1994), 49-62.
12. Gessel, I. M. Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
13. Hisakado, M. Unitary matrix models and Painlevé III. Modern Phys. Lett. A 11 (1996), no. 38, 3001-3010.
14. Johansson, K. On random matrices from the compact classical groups. Ann. of Math. (2) 145 (1997), no. 3, 519-545.
15. Mehta, M. L. Random matrices. Second edition. Academic Press, Boston, 1991.
16. Rains, E. M. Increasing subsequences and the classical groups. Electron. J. Combin. 5 (1998), no. 1, Research Paper 12, 9 pp.
17. Suris, Y. B. A note on an integrable discretization of the nonlinear Schrödinger equation. Inverse Problems 13 (1997), no. 4, 1121-1136.
18. Tracy, C. A.; Widom, H. Random unitary matrices, permutations and Painlevé. Comm. Math. Phys. 207 (1999), no. 3, 665-685.
19. Tracy, C. A.; Widom, H. On the distribution of the lengths of the longest monotone subsequences in random words. Preprint Math. CO/9904042, 1999.