Logarithmic potential beta-ensembles and Feynman graphs

Details Logarithmic potential beta-ensembles and Feynman graphs Logarithmic potential beta-ensembles and Feynman graphs

2010-09-29

arxiv.org/abs/1009.5940v1

Physics

Mathematical Physics

17 pages, 20 figures in text; paper in honor of A.A.Slavnov's 70th birthday

Scientific paper

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power beta by the Vandermonde) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans 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 year 2006.

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