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.

Duality of spectral curves arising in two-matrix models / Bertola, M.; Eynard, B.; Harnad, J.. - In: THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 0040-5779. - 134:1(2003), pp. 27-38. [10.1023/A:1021811505196]

Duality of spectral curves arising in two-matrix models

Bertola, M.;
2003-01-01

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.
2003
134
1
27
38
https://link.springer.com/article/10.1023%2FA%3A1021811505196
Bertola, M.; Eynard, B.; Harnad, J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17099
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