On the distribution of the length of the second row of a young diagram under plancherel measure

Geometric and Functional Analysis

Volumn 10, Issue 4, 2000, Pages 702-731

  Baik, Jinho ^a,b   Deift, Percy ^a,c   Johansson, Kurt ^d  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

^d ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034365262     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001635     Document Type: Article

References (38)

1. J. BAIK, Random vicious walks and random matrices, Comm. Pure Appl. Math., to appear.
2. J. BAIK, P. DEIFT, K. JOHANSSON, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12:4 (1999), 1119-1178.
3. J. BAIK, E. RAINS, Algebraic aspects of increasing subsequences, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9905083.
4. J. BAIK, E. RAINS, The asymptotics of monotone subsequences of involutions, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9905084.
5. J. BAIK, E. RAINS, Limiting distributions for a polynuclear growth model with external sources, J. Statist. Phys., to appear.
6. A. BORODIN, A. OKOUNKOV, G. OLSHANSKI, On asymptotics of Plancherel measures for symmetric groups, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9905032.
7. K. CLANCEY, I. GOHBERG, Factorization of matrix functions and singular integral operators, Birkhäuser, 1981.
8. P.A. DEIFT, Integrable operators, Amer. Math. Soc. Transl. Ser. 2, 189 (1999), 69-84.
9. P.A. DEIFT, A.R. ITS, X. ZHOU, A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics, Ann. Math. 146 (1997), 149-235.
10. P.A. DEIFT, T. KRIECHERBAUER, K.T.-R. MCLAUGHLIN, S. VENAKIDES, X. ZHOU, Asymptotics for polynomials orthogonal with respect to varying exponential weights, Internat. Math. Res. Notices 16 (1997), 759-782; Strong asymptotics for orthogonal polynomials with respect to varying exponential weights via Riemann-Hilbert techniques, Comm. Pure Appl. Math. 52:12 (1999), 1491-1552; Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52:11 (1999), 1335-1425.
11. P.A. DEIFT, T. KRIECHERBAUER, K.T.-R. MCLAUGHLIN, S. VENAKIDES, X. ZHOU, Asymptotics for polynomials orthogonal with respect to varying exponential weights, Internat. Math. Res. Notices 16 (1997), 759-782; Strong asymptotics for orthogonal polynomials with respect to varying exponential weights via Riemann-Hilbert techniques, Comm. Pure Appl. Math. 52:12 (1999), 1491-1552; Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52:11 (1999), 1335-1425.
12. P.A. DEIFT, T. KRIECHERBAUER, K.T.-R. MCLAUGHLIN, S. VENAKIDES, X. ZHOU, Asymptotics for polynomials orthogonal with respect to varying exponential weights, Internat. Math. Res. Notices 16 (1997), 759-782; Strong asymptotics for orthogonal polynomials with respect to varying exponential weights via Riemann-Hilbert techniques, Comm. Pure Appl. Math. 52:12 (1999), 1491-1552; Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52:11 (1999), 1335-1425.
13. P.A. DEIFT, S. VENAKIDES, X. ZHOU, The collisionless shock region for the long-time behavior of solutions of the KdV equation, Comm. Pure Appl. Math. 47:2 (1994), 199-206.
14. P.A. DEIFT, S. VENAKIDES, X. ZHOU, New results in small dispersion KdV by an extension of the steepest descent method for Riemann-Hilbert problems, Internat. Math. Res. Notices 6 (1997), 285-299.
15. P.A. DEIFT, X. ZHOU, A steepest descent method for oscillatory Riemman-Hilbert problems; asymptotics for the MKdV equation, Ann. Math. 137, 295-368. (1993).
16. P.A. DEIFT, X. ZHOU, Asymptotics for the Painlevé II Equation, Comm. Pure. Appl. Math. 48 (1995), 277-337.
17. A.S. FOKAS, A.R. ITS, V.E. KITAEV, Discrete Painlevé equations and their appearance in quantum gravity, Comm. Math. Phy. 142 (1991), 313-344.
18. P. FORRESTER, Random walks and random permutations, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9907037.
19. I.M. GESSEL, Symmetric functions and P-recursiveness, J. Combin. Theory. Ser. A 53 (1990), 257-285.
20. C. GREENE, An extension of Schensted's theorem, Adv. in Math. 14 (1974), 254-265.
21. A.R. ITS, A.G. IZERGIN, V.E. KOREPIN, N.A. SLAVNOV, Differential equations for quantum correlation functions, Int. J. Mod. Phy. B4 (1990), 1003-1037; The quantum correlation functions as the τ function of classical differential equations, 407-417, in "Important Development in Soliton Theory" (A.S. Fokas, V.E. Zakharov, ed.), Springer-Verlag, 1993.
22. A.R. ITS, A.G. IZERGIN, V.E. KOREPIN, N.A. SLAVNOV, Differential equations for quantum correlation functions, Int. J. Mod. Phy. B4 (1990), 1003-1037; The quantum correlation functions as the τ function of classical differential equations, 407-417, in "Important Development in Soliton Theory" (A.S. Fokas, V.E. Zakharov, ed.), Springer-Verlag, 1993.
23. A. ITS, C. TRACY, H. WIDOM, Random words, Toeplitz determinants and integrable systems, I, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9909169.
24. K. JOHANSSON, The longest increasing subsequence in a random permutation and a unitary random matrix model, Math. Res. Lett. 5:1-2 (1998), 63-82.
25. K. JOHANSSON, Shape fluctuations and random matrices, Comm. Math. Phys. 209:2 (1999), 437-476.
26. K. JOHANSSON, Discrete orthogonal polynomial ensembles and the Plancherei measure, Ann. of Math., to appear.
27. T. KATO, Perturbation theory for linear operators, Springer-Verlag, Berlin, 1976.
28. D.E. KNUTH, The Art of Computer Programming, vol. 3: Sorting and Searching, 2nd ed., Addison Wesley, Reading, Mass., 1973.
29. A. OKOUNKOV, Random matrices and random permutations, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9903176.
30. M. PRÄHOFER, H. SPOHN, Statistical self-similarity of one-dimensional growth processes, preprint, 1999, available at http://xxx.lanl.gov/abs/cond-mat/9910273.
31. M. PRÄHOFER, H. SPOHN, Universal distributions for growth processes in 1 + 1 dimensions and random matrices, preprint, 1999, available at http://xxx.lanl.gov/abs/cond-mat/9912264.
32. E.M. RAINS, Increasing subsequences and the classical groups, Electronic J. of Combinatorics 5:1, R12, (1998).
33. B. SAGAN, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Wadsworth&Books/Cole, Pacific Grove, Calif., 1991.
34. C. SCHENSTED, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961), 179-191.
35. R. STANLEY, Generalized riffle shuffles and quasisymmetric functions, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9912025.
36. G. SZEGÖ, Orthogonal Polynomials, American Mathematical Society Colloquium Publications 23, 4th Ed, New York, 1975.
37. C. A. TRACY, H. WIDOM, Level-Spacing distributions and the Airy kernel, Comm. Math. Phys. 159 (1994), 151-174.
38. C. A. TRACY, H. WIDOM, On the distribution of the lengths of the longest monotone subsequences in random words, preprint, 1999, available at http://xxx.lanl.gov/abs/math.CO/9904042.