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

Bertrand Eynard (1) , Nicolas Orantin (1)

1 SPhT - Service de Physique Théorique

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}).

Keywords: Mirzakhani; Kontsevitch; loop equations; matrix models; Weil Petersson; moduli space

Domains: Mathematical Physics [math-ph]; Algebraic Geometry [math.AG]; High Energy Physics - Theory [hep-th]

Bertrand Eynard, Nicolas Orantin. Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models. 2007. ⟨hal-00149179⟩