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Logarithmic potential β-ensembles and Feynman graphs

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To my teacher, Andrei Alekseevich Slavnov, who showed me the beauty of Feynman graphs

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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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    L. O. Chekhov

  2. Alikhanov Institute for Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya ul. 25, Moscow, 117218, Russia

    L. O. Chekhov

  3. Laboratoire J.-V. Poncelet, Bol’shoi Vlas’evskii per. 11, Moscow, 119002, Russia

    L. O. Chekhov

  4. Concordia University, 1455 De Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada

    L. O. Chekhov

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  1. L. O. Chekhov
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Correspondence to L. O. Chekhov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Vol. 272, pp. 65–83.

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Chekhov, L.O. Logarithmic potential β-ensembles and Feynman graphs. Proc. Steklov Inst. Math. 272, 58–74 (2011). https://doi.org/10.1134/S008154381101007X

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  • DOI: https://doi.org/10.1134/S008154381101007X

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