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A matrix model for simple Hurwitz numbers, and topological recursion (0906.1206v1)
Published 5 Jun 2009 in math-ph, hep-th, and math.MP
Abstract: We introduce a new matrix model representation for the generating function of simple Hurwitz numbers. We calculate the spectral curve of the model and the associated symplectic invariants developed in [Eynard-Orantin]. As an application, we prove the conjecture proposed by Bouchard and Marino, relating Hurwitz numbers to the spectral invariants of the Lambert curve exp(x)=y exp(-y).
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