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Tr. Mat. Inst. Steklova, 2011, Volume 272, Pages 65–83 (Mi tm3251)  

This article is cited in 1 scientific paper (total in 1 paper)

Logarithmic potential $\beta$-ensembles and Feynman graphs

L. O. Chekhovabcd

a Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
c Laboratoire J.-V. Poncelet, Moscow, Russia
d Concordia University, Montreal, Quebec, Canada

Abstract: We present a diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with an arbitrary power of the Vandermonde determinant) to all orders of the $1/N$ expansion in the case when the limiting eigenvalue distribution spans an arbitrary (but fixed) number of disjoint intervals (curves) and when logarithmic terms are present. This diagrammatic technique is corrected and refined as compared to our first paper with B. Eynard of 2006.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2011, 272, 58–74

Bibliographic databases:

Document Type: Article
UDC: 530.145
Received in September 2010

Citation: L. O. Chekhov, “Logarithmic potential $\beta$-ensembles and Feynman graphs”, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Collected papers. Dedicated to Academician Andrei Alekseevich Slavnov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 272, MAIK Nauka/Interperiodica, Moscow, 2011, 65–83; Proc. Steklov Inst. Math., 272 (2011), 58–74

Citation in format AMSBIB
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\by L.~O.~Chekhov
\paper Logarithmic potential $\beta$-ensembles and Feynman graphs
\inbook Problems of modern theoretical and mathematical physics: Gauge theories and superstrings
\bookinfo Collected papers. Dedicated to Academician Andrei Alekseevich Slavnov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2011
\vol 272
\pages 65--83
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3251}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2838840}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 272
\pages 58--74
\crossref{https://doi.org/10.1134/S008154381101007X}
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    This publication is cited in the following articles:
    1. Cunden F.D., Mezzadri F., Simm N., Vivo P., “Correlators for the Wigner–Smith time-delay matrix of chaotic cavities”, J. Phys. A-Math. Theor., 49:18 (2016), 18LT01  crossref  mathscinet  zmath  isi  elib  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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