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This article is cited in 16 scientific papers (total in 16 papers)
Duality of Spectral Curves Arising in Two-Matrix Models
M. Bertolaab, B. Eynardac, J. Harnadab a Université de Montréal, Centre de Recherches Mathématiques
b Concordia University, Department of Mathematics and Statistics
c CEA, Service de Physique Théorique
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 $N\to\infty$, we prove that the obtained dual systems have the same spectral curve.
Keywords:
random matrix model, asymptotic analysis, ODE duality.
Citation:
M. Bertola, B. Eynard, J. Harnad, “Duality of Spectral Curves Arising in Two-Matrix Models”, TMF, 134:1 (2003), 32–45; Theoret. and Math. Phys., 134:1 (2003), 27–38
Linking options:
https://www.mathnet.ru/eng/tmf138https://doi.org/10.4213/tmf138 https://www.mathnet.ru/eng/tmf/v134/i1/p32
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Abstract page: | 372 | Full-text PDF : | 199 | References: | 50 | First page: | 1 |
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