A matrix model for simple Hurwitz numbers, and topological recursion

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 and Orantin (2007) [3]. As an application, we prove the conjecture proposed by Bouchard and Mariño (2008) [1], relating Hurwitz numbers to the spectral invariants of the Lambert curve ex=ye−y.