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

Abstract

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.

42 pages, one appendix added, referee comments added, minor typos corrected

References in corpus (1)

• The Cauchy two-matrix model

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