Duality of Spectral Curves Arising in Two-Matrix Models |
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Authors: | Bertola M Eynard B Harnad J |
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Institution: | (1) Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada;(2) Department of Mathematics and Statistics, Concordia University, Montréal, Canada;(3) Service de Physique Théorique, CEA, Saclay, France |
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Abstract: | We consider the two-matrix model with the measure given by the exponential of a sum of polynomials in two different variables. We derive a sequence of pairs of dual finite-size systems of ODEs for the corresponding biorthonormal polynomials. We prove an inverse theorem, which shows how to reconstruct such measures from pairs of semi-infinite finite-band matrices, which define the recursion relations and satisfy the string equation. In the limit N, we prove that the obtained dual systems have the same spectral curve. |
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Keywords: | random matrix model asymptotic analysis ODE duality |
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