New recursive residue formulas for the topological expansion of the Cauchy Matrix Model

Understand

In a recent work [1] we consider the topological expansion for the non-mixed observables (including the free energy) for the formal Cauchy matrix model.

• The only restriction in [1] was the fact that all the branch points have to be simple.
• This excludes a very interesting situation not encountered in the literature before, namely the case in which two branch points merge in such a way that no cycle is pinched.
• In this work we focus on this situation and derive new formulas that apply to non-simple and non-singular branch-points.