Geodesic
Resolvents and Seiberg–Witten representation for a Gaussian $\beta$-ensemble
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 96-115 Cet article a éte moissonné depuis la source Math-Net.Ru

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The exact free energy of a matrix model always satisfies the Seiberg–Witten equations on a complex curve defined by singularities of the semiclassical resolvent. The role of the Seiberg–Witten differential is played by the exact one-point resolvent in this case. We show that these properties are preserved in the generalization of matrix models to $\beta$-ensembles. But because the integrability and Harer–Zagier topological recursion are still unavailable for $\beta$-ensembles, we must rely on the ordinary Alexandrov–Mironov–Morozov/Eynard–Orantin recursion to evaluate the first terms of the genus expansion. We restrict our consideration to the Gaussian model.
Keywords: matrix model, integrability, Seiberg–Witten theory.
Mots-clés : $\beta$-ensemble 
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     title = {Resolvents and {Seiberg{\textendash}Witten} representation for {a~Gaussian} $\beta$-ensemble},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. D. Mironov; A. Yu. Morozov; A. V. Popolitov; Sh. R. Shakirov. Resolvents and Seiberg–Witten representation for a Gaussian $\beta$-ensemble. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 96-115. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a8/

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