A remark on Mirzakhani’s asymptotic formulae. (English) Zbl 1304.30062

Liu, Kefeng; Xu, Hao

Asian J. Math. 18, No. 1, 29-52 (2014).

Summary: 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.

MSC:

30F60	Teichmüller theory for Riemann surfaces
32G15	Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)

Keywords:

Weil-Petersson volumes; moduli spaces of curves