Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

Nuclear Physics B

Volumn 700, Issue 1-3, 2004, Pages 521-532

  Teodorescu, R ^a,g   Bettelheim, E ^a,b   Agam, O ^b   Zabrodin, A ^c,d   Wiegmann, P ^e,f  

^a UNIVERSITY OF CHICAGO   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^c EMANUEL INSTITUTE OF BIOCHEMICAL PHYSICS   (Russian Federation)

^d INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^e UNIVERSITY OF CHICAGO   (United States)

^f LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^g Department of Earth and Environmental Sciences   (United States)

Author keywords

Integrable systems; Random matrix theory

Indexed keywords

EID: 7244227886     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2004.08.013     Document Type: Article

References (39)

1. M. Mineev-Weinstein P.B. Wiegmann A. Zabrodin Phys. Rev. Lett. 84 2000 5106
2. O. Agam E. Bettelheim P.B. Wiegmann A. Zabrodin Viscous fingering and a shape of an electronic droplet in a quantum Hall regime Phys. Rev. Lett. 88 2002 236802
3. I. Krichever M. Mineev-Weinstein P.B. Wiegmann A. Zabrodin Laplacian growth and Whitham equations of soliton theory nlin.SI/0311005
4. R. Teodorescu E. Bettelheim O. Agam A. Zabrodin P. Wiegmann Normal random matrix ensemble as a growth problem hep-th/0401165 Nucl. Phys. B, submitted for publication
5. R. Dijgraaf C. Vafa N = 1 supersymmetry, deconstruction and bosonic gauge theory hep-th/0302011
6. R. Dijgraaf C. Vafa A perturbative window into non-perturbative physics hep-th/0208048
7. R. Dijgraaf C. Vafa Matrix models, topological strings and supersymmetric gauge theories hep-th/0206255
8. R. Dijgraaf C. Vafa On geometry and matrix models hep-th/0207106
9. M. Bertola B. Eynard J. Harnad Partition functions for matrix models and isomonodromic tau functions nlin.SI/0204054
10. A. Kapaev Riemann-Hilbert problem for bi-orthogonal polynomials J. Phys. A 36 2003 4629-4640
11. P. Di Francesco P. Ginsparg J. Zinn-Justin 2-D gravity and random matrices Phys. Rep. 254 1995 1-133
12. A.S. Fokas A.R. Its A. Kitaev The isomonodromy approach to the matrix models in 2-D gravity Commun. Math. Phys. 147 1992 395-430
13. V.A. Kazakov A. Marshakov Complex curve of the two matrix model and its tau-function J. Phys. A 36 2003 3107-3136
14. L. Chekhov A. Mironov Matrix models vs. Seiberg-Witten/Whitham theories hep-th/0209085
15. L.-L. Chau O. Zaboronsky On the structure of normal matrix model Commun. Math. Phys. 196 1998 203-247 hep-th/9711091
16. M.L. Mehta Random Matrices 1991 Academic Press New York
17. P.B. Wiegmann A. Zabrodin Large scale correlations in normal and general non-hermitian matrix ensembles J. Phys. A 36 2003 3411-3424
18. H. Aratyn Integrable Lax hierarchies, their symmetry reductions and multi-matrix models hep-th/9503211
19. M. Bertola B. Eynard J. Harnad Duality of spectral curves arising in two-matrix models nlin.SI/0112006
20. M. Bertola B. Eynard J. Harnad Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem nlin.SI/0208002
21. W. Wasow Asymptotic Expansions for Ordinary Differential Equations 1965 Wiley New York
22. B.A. Dubrovin I.M. Krichever S.P. Novikov Topological and algebraic geometry methods in contemporary mathematical physics II Soviet Sci. Rev. Math. Phys. Rev. 3 1982 1-150
23. I.M. Krichever Integration of nonlinear equations by the method of algebraic geometry Functional Anal. Appl. 11 1977 12-26
24. L.V. Ahlfors Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable 1953 McGraw-Hill New York
25. H. Cohn Conformal Mapping on Riemann Surfaces 1967 Dover New York
26. M. Schiffer D.C. Spencer Functionals of Finite Riemann Surfaces 1954 Princeton Univ. Press Princeton, NJ
27. I.K. Kostov I. Krichever M. Mineev-Weinstein P.B. Wiegmann A. Zabrodin τ-function for analytic curves in: Random Matric Models and Their Applications in: Mathematical Sciences Research Institute Publications vol. 40 2001 Cambridge Univ. Press Cambridge 285
28. A. Marshakov A. Mironov A. Morozov Generalized matrix models as conformal field theories: Discrete case Phys. Lett. B 265 1991 99
29. S. Kharchev A. Marshakov A. Mironov A. Morozov S. Pakuliak Conformal matrix models as an alternative to conventional multimatrix models Nucl. Phys. B 404 1993 717 hep-th/9208044
30. K. Ueno K. Takasaki Adv. Stud. Pure Math. 4 1984 1
31. J.B. Whitham Linear and Nonlinear Waves 1974 Wiley-Interscience New York
32. H. Flaschka M.G. Forest D.W. McLaughlin Multiphase averaging and the inverse spectral solution of the Korteweg-de Vries equation Commun. Pure Appl. Math. 33 1980 739-784
33. I.M. Krichever Method of averaging for two-dimensional "integrable"; equations Functional Anal. Appl. 22 1988 200-213
34. L.A. Galin Dokl. Akad. Nauk SSSR 47 1945 250-253
35. P.Ya. Polubarinova-Kochina Dokl. Akad. Nauk SSSR 47 1945 254-257
36. P.P. Kufarev Dokl. Akad. Nauk SSSR 57 1947 335-348
37. P.B. Wiegmann A. Zabrodin Conformal maps and dispersionless integrable hierarchies Commun. Math. Phys. 213 2000 523-538
38. A. Marshakov P.B. Wiegmann A. Zabrodin Integrable structure of the Dirichlet boundary problem in two dimensions Commun. Math. Phys. 227 2002 131-153
39. I. Krichever A. Marshakov A. Zabrodin Integrable structure of the Dirichlet boundary problem in multiply-connected domains hep-th/0309010