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Duality of spectral curves arising in two-matrix models

M. Bertola·B. Eynard·J. Harnad
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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.

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M. Bertola, B. Eynard, J. Harnad. 2001-12-05. Duality of spectral curves arising in two-matrix models. https://arxiv.org/abs/nlin/0112006

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