Geodesic
Duality of Spectral Curves Arising in Two-Matrix Models
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 32-45

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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 $N\to\infty$, we prove that the obtained dual systems have the same spectral curve.
Keywords: random matrix model, asymptotic analysis, ODE duality. 
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     author = {M. Bertola and B. Eynard and J. Harnad},
     title = {Duality of {Spectral} {Curves} {Arising} in {Two-Matrix} {Models}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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M. Bertola; B. Eynard; J. Harnad. Duality of Spectral Curves Arising in Two-Matrix Models. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 32-45. http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a3/