Increasing subsequences and the hard-to-soft edge transition in matrix ensembles

Journal of Physics A: Mathematical and General

Volumn 36, Issue 12 SPEC. ISS., 2003, Pages 2963-2981

  Borodin, Alexei ^a   Forrester, Peter J ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037471252     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/12/307     Document Type: Article

References (38)

1. Aldous D and Hammersley P D 1995 Interacting particle process and longest increasing subsequences Probab. Theory Rel. Fields 103 199-213
2. Aldous D and Diaconis P 1999 Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem Bull. Am. Math. Soc. 36 413-32
3. Baik J, Dieft F and Johansson K 1999 On the distribution of the length of the longest increasing subsequence of random permutations J. Am. Math. Soc. 12 1119-78
4. Baik J and Rains E M 2001 Algebraic aspects of increasing subsequences Duke Math. J. 109 1-65
5. Baik J and Rains E M 2001 The asymptotics of monotone subsequences of involutions. Duke Math. J. 109 205-81
6. Borodin A 1999 Biorthogonal ensembles Nucl. Phys. B 536 704-32
7. Borodin A, Okounkov A and Olshanski G 2000 On asymptotics of Plancherel measures for symmetric groups J. Am. Math. Soc. 13481-515
8. Dueñez E 2001 Random matrix ensembles associated to compact symmetric spaces Preprint math-ph/0111005
9. Dumitriu I and Edleman A 2002 Matrix models for beta ensembles J. Math. Phys. 43 5830-47
10. Forrester P J 1993 Exact results and universal asymptotics in the Laguerre random matrix ensemble J. Math. Phys. 35 2539-51
11. Forrester P J 1993 The spectrum edge of random matrix ensembles Nucl. Phys. B 402 709-28
12. Forrester P J 2000 Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles Preprint nlin.SI/0005064
13. Forrester P J Log-gases and random matrices webpage www.ms.unimelb.edu.au/̃matpjf/matpjf.html.
14. Forrester P J and Hughes T D 1994 Complex Wishart matrices and conductance in mesoscopic systems: exact results j. Math. Phys. 35 6736-47
15. Forrester P J, Nagao T and Honner G 1999 Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges Nucl. Phys. B 553 601-43
16. Forrester P J and Rains E M 2002 Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter Preprint math-ph/0211041
17. Forrester P J and Witte N S 2002 Application of the τ-function theory of Painlevé equations to random matrices: PVI, the JUE,CyUE, cJUE and scaled limits Preprint math-ph/0204008
18. James A T 1964 Distribution of matrix variates and latent roots derived from normal samples Ann. Math. Stat. 35 475-501
19. Johansson K 1998 The longest increasing subsequence in a random permutation and a unitary random matrix model Math. Res. Lett. 5 63-82
20. Johansson K 2000 Shape fluctuations and random matrices Commun. Math. Phys. 209 437-76
21. Johansson K 2001 Discrete orthogonal polynomial ensembles and the Plancherel measure Ann. Math. 153 259-96
22. Johnstone I M 2001 On the distribution of the largest eigenvalue in principal components analysis Ann. Stat. 29 295-327
23. Kaneko J 1993 Selberg integrals and hypergeometric functions associated with Jack polynomials SIAM J. Math Anal. 24 1086-110
24. Lenard A 1973 Correlation functions and the uniqueness of the state in classical statitical mechanics Commun. Math. Phys. 30 35-44
25. Macdonald I G 1995 Hall Polynomials and Symmetric Functions 2nd edn (Oxford: Oxford University Press)
26. Muirhead R J 1982 Aspects of Multivariable Statistical Theory (New York: Wiley)
27. Okounkov A 2000 Random matrices and random permutations Int. Math. Res. Notices 20 1043-95
28. Olver F W J 1974 Asymptotics and Special Functions (New York: Academic)
29. Rains E M 1995 Attack of the zonal polynomials Preprint
30. Rains E M 1998 Increasing subsequences and the classical groups Elect. J. Combinat. 5 #R12
31. n-symmetric polynomials Preprint math.QA/0112035
32. Soshnikov A 2000 Determinantal random point fields Russian Math. Surveys 55 923-75
33. Soshnikov A 2001 A note on the universality of the distribution of the largest eigenvalues in certain sample covariance matrices Preprint math.PR/0104113
34. Stanley R P 1989 Some combinatorial properties of Jack symmetric functions Adv. Math. 77 76-115
35. Tracy C A and Widom H 1994 Level-spacing distributions and the Airy kernel Commun. Math. Phys. 159 151-74
36. Tracy C A and Widom H 1994 Level-spacing distributions and the Bessel kernel Commun. Math. Phys. 161 289-309
37. Tracy C A and Widom H 1996 On orthogonal and symplectic matrix ensembles Commun. Math. Phys. 177 727-54
38. Whittaker E T and Watson G N 1965 A Course of Modern Analysis 2nd edn (Cambridge: Cambridge University Press)