Random unitary matrices, permutations and Painlevé

Communications in Mathematical Physics

Volumn 207, Issue 3, 1999, Pages 665-685

  Tracy, Craig A ^a   Widom, Harold ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033474974     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050741     Document Type: Article

References (11)

1. 1. Baik, J.,Deift, P. and Johansson, K.: On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc 12, 1119-1178 (1999)
2. 2. Deift, P.A. and Zhou, X.: Asymptotics for the Painlevé II equation. Comm. Pure Appl. Math. 48, 277-337 (1995)
3. 3. Gessel, I.M.: Symmetric functions and P-recursiveness. J. Combin. Th. Ser. A 53, 257-285 (1990)
4. 4. Hisakado, M.: Unitary matrix models and Painlevé III. Mod. Phys. Letts A11, 3001-3010 (1996)
5. 5. Johansson, K.: The longest increasing subsequence in a random permutation and a unitary random matrix model. Math. Res. Lett. 5, 63-82 (1998)
6. 6. Nijhoff, F.W. and Papageorgiou, V.G.: Similarity reductions of integrable lattices and discrete analogues of the Painlevé II equation. Phys. Lett. 153A, 337-344 (1991)
7. 7. Odlyzko, A.M., Poonen, B., Widom, H. and Wilf, H.S.: On the distribution of longest increasing subsequences in random permutations. Unpublished notes
8. 8. Okamoto, K.: Polynomial Hamiltonians associated with Painlevé equations. Proc. Japan Acad. A56, 367-371 (1980)
9. 9. Periwal, V. and Shevitz, D.: Unitary-matrix models as exactly solvable string theories. Phys. Rev. Lett. 64, 1326-1329 (1990)
10. 10. Rains, E.M.: Increasing subsequences and the classical groups. Elect. J. of Combinatorics 5, #R12 (1998)
11. 11. Tracy, C.A. and Widom, H.: Level-spacing distributions and the Airy kernel. Commun. Math. Phys. 159, 151-174 (1994)