Asian Journal of Mathematics

Volume 18 (2014)

Number 1

A remark on Mirzakhani’s asymptotic formulae

Pages: 29 – 52

DOI: https://dx.doi.org/10.4310/AJM.2014.v18.n1.a2

Authors

Kefeng Liu (Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China; Department of Mathematics, University of California at Los Angeles)

Hao Xu (Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China; Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

We give a short proof of Penner-Grushevsky-Schumacher-Trapani’s large genus asymptotics of Weil-Petersson volumes of moduli spaces of curves. We also study asymptotic expansions for certain integrals of pure $\psi$ classes and answer a question of Mirzakhani on the asymptotic behavior of one-point volume polynomials of moduli spaces of curves.

Keywords

Weil-Petersson volumes, moduli spaces of curves

2010 Mathematics Subject Classification

14H10, 14N10

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Published 13 May 2014