Partition functions for matrix models and isomonodromic tau functions

Journal of Physics A: Mathematical and General

Volumn 36, Issue 12 SPEC. ISS., 2003, Pages 3067-3083

  Bertola, M ^a,b   Eynard, B ^a,c   Harnad, J ^a,b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b Gina Cody School of Engineering and Computer Science   (Canada)

^c CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037471328     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/12/313     Document Type: Article

References (37)

1. Adler M, van Moerbeke P and Shiota T 1998 Random matrices, Virasoro algebras and noncommutative KP Duke Math. J. 94 379-431
2. Adler M and van Moerbeke P 2001 Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum Ann. Math. 153 149-89
3. Aratyn H and van de Leur J 2001 Integrable structure behind WDVV equations Contribution to NEEDS 2001 Conference Preprint hep-th/0111243 (2002 Theor. Math. Phys. at press)
4. Bauldry W 1990 Estimates of asymmetric Freud polynomials on the real line J. Approx. Theory 63 225-37
5. Bertola M, Eynard B and Harnad J 2002 Duality, biorthogonal polynomials and multi-matrix models Commun. Math. Phys. 229 73-120 (CRM-2749 Saclay-T01/047 nlin.SI/0108048)
6. Bleher P and Its A 1999 Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model Ann. Math. 150 185-266
7. Bleher P and Its A 1999 On asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert method Symmetries and Integrability of Difference Equations (Canterbury, 1996) (London Math. Soc. Lecture Note Ser., vol 255) (Cambridge: Cambridge University Press) pp 165-77
8. Bonan S S and Clark D S 1990 Estimates of the Hermite and the Freud polynomials J. Approx. Theory 63 210-24
9. Borodin A and Deift P 2002 Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory Commun. Pure Appl. Math. 55 1160-230
10. Di Francesco P, Ginsparg P and Zinn-Justin J 1995 2D gravity and random matrices Phys. Rep. 254 1
11. Douglas M R and Shenker S H 1990 Strings in less than one dimension Nucl. Phys. B 335 635-54
12. Douglas M R 1990 Strings in less than one dimension and the generalized KdV hierarchies Phys. Lett. B 238 176-80
13. Eynard B 2000 An introduction to random matrices Lectures given at Saclay (Oct. 2000) Notes available at http://www-spht.cea.fr/articles/t01/014
14. Fokas A, Its A and Kitaev A 1992 The isomonodromy approach to matrix models in 2D quantum gravity Commun. Math. Phys. 147 395-430
15. Gerasimov A, Marshakov A, Mironov A, Morozov A and Orlov A 1991 Matrix models of two-dimensional gravity and Toda theory Nucl. Phys. B 357 565-618
16. Harnad J 2002 On the bilinear equations for Fredholm determinants appearing in random matrices J. Nonlinear Math. Phys. 9 530-50
17. Harnad J and Its A R 2002 Integrable Fredholm operators and dual isomonodromic deformations Commun. Math. Phys. 226 497-530
18. Harnad J, Tracy C A and Widom H 1993 Hamiltonian structure of equations appearing in random matrices Low Dimensional Topology and Quantum Field Theory ed H Osborn (New York: Plenum) pp 231-45
19. Ismail M E H and Chen Y 1997 Ladder operators and differential equations for orthogonal polynomials J. Phys. A: Math. Gen. 30 7818-29
20. Its A R, Kitaev A V and Fokas A S 1991 Matrix models of two-dimensional quantum gravity and isomonodromy solutions of discrete Painleve equations Zap. Nauch. Sem. LOMI 187 3-30 (in Russian) (Engl. transl. 1995 J. Math. Sci. 73 415-29)
21. Its A R, Kitaev A V and Fokas A S 1991 Matrix models of two-dimensional quantum gravity and isomonodromy solutions of discrete Painleve equations Zap. Nauch. Sem. LOMI 187 3-30 (in Russian) (Engl. transl. 1995 J. Math. Sci. 73 415-29)
22. Its A R, Kitaev A V and Fokas A S 1990 An isomonodromic approach in the theory of two-dimensional quantum gravity Usp. Matem. Nauk 45 135-6 (in Russian) (Engl. transl. 1990 Russ. Math. Surveys 45 155-7)
23. Its A R, Kitaev A V and Fokas A S 1990 An isomonodromic approach in the theory of two-dimensional quantum gravity Usp. Matem. Nauk 45 135-6 (in Russian) (Engl. transl. 1990 Russ. Math. Surveys 45 155-7)
24. Jimbo M, Miwa T and Ueno K 1981 Monodromy preserving deformation of linear ordinary differential equations with rational coefficients I Physica D 2 306-52
25. Marcellán F and Rocha I A 1998 Complex path integral representation for semiclassical linear functionals J. Approx. Theory 94 107-27
26. Marcellán F and Rocha I A 1995 On semiclassical linear functionals: integral representations J. Comput. Appl. Math. 57 239-49
27. Mehta M L 1991 Random Matrices 2nd edn (New York: Academic)
28. Moore G 1990 Geometry of the string equations Commun. Math. Phys. 133 261-304
29. Morozov A 1999 Matrix models as integrable systems Particles and Fields (Banff, AB, 1994) (CRM Ser. Math. Phys.) (New York: Springer) pp 127-210
30. Palmer J 1994 Deformation analysis of matrix models Physica D 78 166-85
31. Sato M and Sato Y 1983 Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold Nonlinear Partial Differential Equations in Applied Science (Tokyo, 1982) (North-Holland Math. Stud. vol 81) (Amsterdam: North-Holland) pp 259-71
32. Segal G and Wilson G 1985 Loop groups and equations of KdV type Inst. Hautes Études Sci. Publ. Math. 61 5-65
33. Szegö G 1939 Orthogonal Polynomials (Providence, RI: AMS)
34. Tracy C A and Widom H 1993 Introduction to random matrices Geometric and Quantum Methods in Integrable Systems (Springer Lecture Notes in Physics vol 424) ed G F Helminck (New York: Springer) pp 103-30
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. van Moerbeke P 1997 The spectrum of random matrices and integrable systems Group21 Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras vol II, ed H-D Doebner, W Scherer and C Schulte (Singapore: World Scientific) pp 835-52