Duality of spectral curves arising in two-matrix models

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dc.creatorBertola, M.
dc.creatorEynard, B.
dc.creatorHarnad, J.
dc.date2001-12-04
dc.date2001-12-05
dc.date.accessioned2026-07-07T05:33:47Z
dc.date.available2026-07-07T05:33:47Z
dc.descriptionThe 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.
dc.descriptionWrite-up based on lecture by J. Harnad given at NEEDS 2001 Euroconference Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. July 24-31, 2001
dc.identifierhttps://arxiv.org/abs/nlin/0112006
dc.identifierhttp://arxiv.org/abs/nlin/0112006
dc.identifierTheor.Math.Phys. 134 (2003) 27-38; Teor.Mat.Fiz. 134 (2003) 32-45
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80127
dc.subjectExactly Solvable and Integrable Systems
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleDuality of spectral curves arising in two-matrix models
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