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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 1, Pages 32–45
DOI: https://doi.org/10.4213/tmf138
(Mi tmf138)
 

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
References:
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.
English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 1, Pages 27–38
DOI: https://doi.org/10.1023/A:1021811505196
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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\paper Duality of Spectral Curves Arising in Two-Matrix Models
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\zmath{https://zbmath.org/?q=an:1068.81044}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 134
\issue 1
\pages 27--38
\crossref{https://doi.org/10.1023/A:1021811505196}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000181042100003}
Linking options:
  • https://www.mathnet.ru/eng/tmf138
  • https://doi.org/10.4213/tmf138
  • https://www.mathnet.ru/eng/tmf/v134/i1/p32
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :199
    References:50
    First page:1
     
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