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

Bertrand Eynard; Nicolas Orantin

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arXiv · 0705.3600

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

Bertrand Eynard·Nicolas Orantin

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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}).

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Bertrand Eynard, Nicolas Orantin. 2007-05-24. Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models. https://arxiv.org/abs/0705.3600

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