Topological expansion of mixed correlations in the Hermitian 2-matrix model andx–ysymmetry of theFgalgebraic invariants

We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. a generating function for counting bicolored discrete surfaces with non-uniform boundary conditions. As an application, we prove the x – y symmetry of Eynard and Orantin (2007 Invariants of algebraic curves and topological expansion Preprint math-ph/0702045).