Abstract
In this paper, we study in detail the modified topological recursion of the one-matrix model for arbitraryβ in the one-cut case. We show that, for polynomial potentials, the recursion can becomputed as a sum of residues. However, the main difference with the Hermitian matrixmodel is that the residues cannot be set at the branch points of the spectral curve butrequire the knowledge of the whole curve. In order to establish non-ambiguous formulae, weplace ourselves in the context of the globalizing parameterization which is specific to theone-cut case (also known as Zhukovsky parameterization). This situation is particularlyinteresting for applications since in most cases the potentials of the matrix models onlyhave one cut in string theory. Finally, the paper exhibits some numerical simulations ofhistograms of the limiting density of eigenvalues for different values of the parameterβ.
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