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.
Kefeng Liu. Hao Xu. "A remark on Mirzakhani's asymptotic formulae." Asian J. Math. 18 (1) 29 - 52, January 2014.