Publication: A Common integrable structure in the hermitian matrix model and Hele-Shaw flows
Loading...
Official URL
Full text at PDC
Publication Date
2008-10
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Atlantis Press
Abstract
It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in HeleShaw flows.
Description
©Atlantis Press.
The authors wish to thank the Spanish Ministerio de Educacion y Ciencia (research project FIS2005-00319) and the European Science Foundation (MISGAM programme) for their financial support.
UCM subjects
Unesco subjects
Keywords
Citation
[1] A. Gerasimov, A. Marshakov, A. Mironov, A. Morozov and A. Orlov, Nuc. Phys. B 357, 565 (1991)
[2] S. Y. Alexandrov, V. A. Kazakov and I. K. Kostov, Nuc. Phys. B 667, 90 (2003)
[3] M. Adler and P. Van Moerbeke, Comm. Math. Phys. 203 , 185 (1999); Comm. Math. Phys. 207 , 589 (1999)
[4] K. Takasaki and T. Takebe, Rev. Math. Phys. 7, 743 (1995)
[5] P. W. Wiegmann and P. B. Zabrodin, Comm. Math. Phys. 213 , 523 (2000)
[6] M. Mineev-Weinstein, P. Wiegmann and A. Zabrodin, Phys. Rev. Lett. 84, 5106
[7] O. Agam, E. Bettelheim, P. Wiegmann and A. Zabrodin, Phys. Rev. Lett. 88, 236801 (2002)
[8] R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin and P. Wiegmann, Nuc. Phys. B 700, 521 (2004); Nuc. Phys. B 704, 407 (2005)
[9] I. Krichever, M. Mineev-Weinstein, P. Wiegmann and A. Zabrodin, Physica D 198, 1 (2004)
[10] S-Y. Lee, E. Bettelheim and P. Wiegmann, Physica D 219, 23(2006)
[11] L. MartÃnez Alonso and E. Medina, Phys. Lett. B 610, 227 (2005)
[12] L. MartÃnez Alonso, M. Mañas and E. Medina, J. Math. Phys. 47, 83512 (2006)
[13] P. Di Francesco, P. Ginsparg and Z. Zinn-Justin , 2D Gravity and Random Matrices hepth/9306153.
[14] B. Eynard, An introduction to random matrices, lectures given at Saclay, October 2000, http://www-spht.cea.fr/articles/t01/014/. [15] E. Brézin, C. Itzikson, G. Parisi and B. Zuber, Comm. Math. Phys. 59 , 35 (1978)
[16] D. Bessis, C. Itzikson, G. Parisi and B. Zuber, Adv. in Appl. Math. 1 , 109 (1980)
[17] C. Itzikson and B. Zuber, J. Math. Phys. 21 , 411 (1980)
[18] A. A. Migdal, Phys. Rep. 102, 199 (1983)