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Bleher","submitted_at":"2016-06-14T10:55:35Z","abstract_excerpt":"We prove the topological expansion for the cubic log-gas partition function \\[ Z_N(t)= \\int_\\Gamma\\cdots\\int_\\Gamma\\prod_{1\\leq j<k\\leq N}(z_j-z_k)^2 \\prod_{k=1}^Ne^{-N\\left(-\\frac{z^3}{3}+tz\\right)}\\mathrm dz_1\\cdots \\mathrm dz_N, \\] where $t$ is a complex parameter and $\\Gamma$ is an unbounded contour on the complex plane extending from $e^{\\pi \\mathrm i}\\infty$ to $e^{\\pi \\mathrm i/3}\\infty$. 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