Duality of spectral curves arising in two-matrix models
Bertola M. (
Centre de Recherches Mathématiques (CMR), Université de Montréal C.P. 6128, succ. centre ville, Montréal, Québec H3C 3J7, CANADA)
Eynard B. (
CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Harnad J. (
Centre de Recherches Mathématiques (CMR), Université de Montréal C.P. 6128, succ. centre ville, Montréal, Québec H3C 3J7, CANADA)
Abstract:
The two matrix model is considered with measure given by the
exponential of a sum of polynomials in two different variables. It is
shown how to derive a sequence of pairs of ``dual'' finite size
systems of ODEs for the corresponding biorthonormal polynomials. An
inverse theorem is proved showing how to reconstruct such measures
from pairs of semi-infinite finite band matrices defining the
recursion relations and satisfying the string equation.
A proof is given in the $N\to \infty$ limit that the dual systems
obtained share the same spectral curve.
Année de publication : 2003
Revue : Theor. Math. Phys.
134
27-38
(2003)
Communication : in: Procedings 2001 of the 15th Euroconference on Nonlinear
Evolution Equations and Dynamical Systems (NEEDS 2001)
;
Cambridge, UK
; 2001-07-24 / 2001-07-31
Preprint :
arXiv:nlin.SI/0112006 Numéro Exterieur : CRM-2828_(novembre_2001)
Langue : Anglais
NB : Teor. Mat. Fiz. 134, 32-45,2003
Fichier(s) à télécharger : publi.pdf