Painlevé v and the distribution function of a discontinuous linear statistic in the Laguerre unitary ensembles

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 3, 2009, Pages

  Basor, Estelle ^a   Chen, Yang ^b  

^a AMERICAN INSTITUTE OF MATHEMATICS   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64549129485     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/3/035203     Document Type: Article

References (31)

1. Akhiezer N I 1964 Continual analogue to some theorems on Toeplitz matrices Am. Math. Soc. Trans. Ser. 50 295-316
2. Basor E and Chen Y 2008 Toeplitz determinants from compatibility conditions Ramanujan J. 16 25-40
3. Bonan S and Nevai P 1984 Orthogonal polynomials and their derivatives: I J. Approx. Theory 40 134-47
4. m), m and even integer J. Approx. Theory 46 408-10
5. Bonan S, Lubinsky D S and Nevai P 1987 Orthogonal polynomials and their derivatives: II J. Approx. SIAM J. Math. Anal. 18 1163-76
6. Basor E L, Chen Y and Widom H 2001 Determinants of Hankel matrices J. Funct. Anal. 179 214-34
7. Basor E L, Ehrhardt T and Widom H 2003 On the determinant of a certain Wiener-Hopf + Hankel operator Integral Eqns Operator Theory 47 275-88
8. Basor E L and Widom H 1983 Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols J. Funct. Anal. 50 387-413
9. Basor E L and Widom H 2005 Wiener-Hopf determinants with Fisher-Hartwig symbols Operator Theoretical Methods and Applications to Mathematical Physics (Oper. Theory Adv. Appl. vol 147) (Basel: Birkhauser) 131-49
10. Böttcher A and Silbermann B 1990 Analysis of Toeplitz Operators (Berlin: Springer)
11. Böttcher A, Silbermann B and Widom H 1994 A continuous analogue of the Fisher-Hartwig formula for piecewise continuous symbols J. Funct. Anal. 122 222-46
12. Böttcher A, Silbermann B and Widom H 1994 Determinants of truncated Wiener-Hopf operators with Hilbert-Schmidt kernels and piecewise continuous symbols Arch. Math. 63 60-71
13. Chen Y and Ismail M 1997 Ladder operators and differential equations for orthogonal polynomials J. Phys. A: Math. Gen. 30 7817-29
14. Chen Y and Ismail M 2005 Jacobi polynomials from compatibility conditions Proc. Am. Math. Soc. 133 465-72
15. Chen Y and Pruessner G 2005 Orthogonal polynomials with discontinuous weights J. Phys. A: Math. Gen. 38 L191-8
16. Gromak V I, Laine I and Shinomura S 2002 Painlevé Differential Equations in the Complex Plane (New York: Springer)
17. Jimbo M and Miwa T 1981 Monodromy preserving deformation of linear ordinary differential equations with rational coefficients: II Physica D 2 407-48
18. Okamoto K 1982 On the τ-function of the Painlevé equations Physica D 2 525-35
19. Kac M 1954 Toeplitz matrices, translation kernel and a related problem in probability theory Duke Math. J. 21 501-9
20. Magnus A P 1995 Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials J. Comput. Appl. Math. 57 215-37
21. Magnus A P 2006 Freud equations for Legendre polynomials on a circular arc and solution of the Grübaum-Delsarte-Janssen-Vries problem J. Approx. Theory 139 75-90
22. Magnus A P 1995 Asymptotics for the simplest generalized Jacobi polynomials recurrence coefficients from Freud's equations: numerical exploration Ann. Numer. Math. 2 311-25
23. Mehta M L 2006 Random Matrices 3rd edn (Singapore: Elsevier)
24. Mikaelyan L V 1986 Asymptotics of determinants of truncated Wiener-Hopf operators in a singular case Akad. Nauk Arm. SSR Dokl. 82 151-5 (in Russian)
25. V Japan. J. Math. (N. S.) 13 47-76
26. Sakai H 2001 Rational surfaces associated with affine root systems and geometry of the Painlevé equations Commun. Math. Phys. 220 165-229
27. Shohat J 1939 A differential equation for orthogonal polynomials Duke Math. J. 5 401-17
28. Sogo K 1993 Time dependent orthogonal polynomials and theory of soliton-applications to matrix model, vertex model and level statistics J. Phys. Soc. Japan 62 1887-94
29. Szegö G 1975 Orthogonal Polynomials (Am. Math. Soc. Colloq. Publ. vol 23) Fourth ed (Providence, RI: American Mathematical Society)
30. Tracy C A and Widom H 1994 Fredholm determinants, differential equations and matrix models Commun. Math. Phys. 163 33-72
31. Tsuda T, Okamoto K and Folding Sakai H 2005 Transformations of the Painlevé equations Math. Ann. 331 713-38