Painlevé v and time-dependent Jacobi polynomials

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 1, 2010, Pages

  Basor, Estelle ^a   Chen, Yang ^b   Ehrhardt, Torsten ^c  

^a AMERICAN INSTITUTE OF MATHEMATICS   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 73249150106     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/1/015204     Document Type: Article

References (35)

1. Adler M and van Moerbeke P 1995 Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials Duke Math. J. 80 863-911
2. Barnes E W 1900 The theory of the G-function Q. J. Pure Appl. Math. 31 264
3. Basor E L and Chen Y 2005 Perturbed Hankel determinants J. Phys. A.: Math. Gen. 38 10101-6
4. Basor E L and Chen Y 2009 Painlevé V and the distribution function of a discontinuous linear statistics in the Laguerre unitary ensembles J. Phys. A: Math. Theor. 42 035203
5. Basor E L and Ehrhardt T 2002 Some identities for determinants of structured matrices Linear Algebr. Appl. 343-344 5-19
6. Basor E L and Ehrhardt T 2009 Determinant computations for some classes of Toeplitz-Hankel matrices Oper. Matrices 3 167-86
7. Bauldry W 1990 Estimate of the asymmetric Freud polynomials J. Approx. Theory 63 225-37
8. Belmehda S and Ronveaux A 1994 Laguerre-Freud's equations for the recurrence coefficients of semi-classical orthogonal polynomials J. Approx. Theory 76 351-68
9. Bonan S and Nevai P 1984 Orthogonal polynomials and their derivatives. I J. Approx. Theory 40 134-47
10. m), m an even positive integer J. Approx. Theory 46 408-10
11. Bonan S and Clark D S 1990 Estimates of the Hermite and Freud polynomials J. Approx. Theory 63 210-24
12. Chen Y and Dai D 2008 Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials arXiv:0809.3641v2
13. Chen Y and Ismail M E H 1997 Ladder operators and differential equations for orthogonal polynomials J. Phys. A: Math. Gen. 30 7817-29 (Pubitemid 127375455)
14. Chen Y and Ismail M E H 1997 Thermodynamic relations of the Hermitian matrix ensembles J. Phys. A.: Math. Gen. 30 6633-54
15. Chen Y and Ismail M E H 2005 Jacobi polynomials from campatibilty conditions Proc. Am. Math. Soc. 133 465-72
16. Chen Y and Lawrence N D 1998 On the linear statistics of Hermitean random matrices J. Phys. A.: Math. Gen. 31 1141-52
17. Chen Y and Its A 2008 Painlevé III and a singular linear statistics in Hermitean random matrix ensemlbes. I J. Approx. Theory (arXiv:0808.3590v2)
18. Chen Y and Feigin M V 2006 Painlevé IV and degenerate Gaussian unitary ensembles J. Phys. A: Math. Gen. 39 12381-93
19. Chen Y and Pruessner G 2005 Orthogonal polynomials with discontinuous weights J. Phys. A: Math. Gen. 38 L191-8
20. Fokas A S, Its A R and Kitaev A V 1991 Discrete Painlevé equations and their appearance in quantum gravity Commun. Math. Phys. 142 313-44
21. Fokas A S, Its A R and Kitaev A V 1992 The isomonodromy approach to matrix models in 2D gravity Commun. Math. Phys. 147 395-430
22. Forrester P J and Witte N S 2007 The distribution of the first eigenvalue at the hard edge of the Laguerre unitary ensembles Kyushu Math. J. 61 457-526
23. Haine L and Horozov E 1993 Toda orbits of Laguerre polynomials and representations of the Virasoro algebra Bull. Sci. Math. 17 485-518
24. Haine L and Semengue J-P 1999 The Jacobi polynomial ensembles and the Painlevé equation J. Math. Phys. 40 2117-34
25. Jimbo M and Miwa T 1981 Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II Physica D 2 407-48
26. Magnus A P 1995 Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials J. Comput. Appl. Math. 57 215-37
27. Masuda T 2004 Classical transcendental solutions of the Painlevé equations and their degeneration Tohoku Math. J. 56 467-90
28. Mehta M L 2004 Random Matrices 3rd edn (Amsterdam: Elsevier)
29. Moser J 1975 Finitely many mass points on the line under the influence of an exponential potential-an integrable system Dynamical Systems, Theory and Applications vol 38 (Lecture Notes in Physics) ed J Moser (Berlin: Springer) pp 467-97
30. V Japan. J. Math. (N.S.) 13 47-76
31. Tsuda T, Okamoto K and Sakai H 2005 Folding transformation of the Painlevé equations Math. Ann. 331 713-38
32. Sogo K 1993 Time dependent orthogonal polynomials and theory of solition-applications to matrix model, vertex model and level statistics J. Phys. Soc. Japan 62 1887-94
33. Szegö G 1975 Orthogonal Polynomials vol 23 (Providence, RI: Am. Math. Soc.)
34. Tracy C A and Widom H 1994 Fredholm determinants, differential equations and matrix models Commun. Math. Phys. 163 33-72
35. Witten E 1991 Two-dimensional gravity and intersection thoery on moduli space Surveys in Differential Geometry 1 (supplement to J. Diff. Geom.) ed C C Hsiung and S T Yau pp 243-310