Publication : t01/123
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:Année de publication : 2003
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.
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
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