Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants

Abstract

We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. generating function for counting bicolored discrete surfaces with non uniform boundary conditions. As an application, we prove the $x-y$ symmetry of the algebraic curve invariants introduced in math-ph/0702045.