Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models

Abstract

We show that Mirzakhani's recursions for the volumes of moduli space of Riemann surfaces are a special case of random matrix loop equations, and therefore we confirm again that Kontsevitch's integral is a generating function for those volumes. As an application, we propose a formula for the Weil-Petersson volume Vol(M_{g,0}).

arXiv commentLatex, 9 pages

References in corpus (2)

• All genus correlation functions for the hermitian 1-matrix model
• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy

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