Recursions and Asymptotics of Intersection Numbers

We establish the asymptotic expansion of certain integrals of ψ classes on moduli spaces of curves Mg,n when either the g or n goes to infinity. Our main tools are cut-join type recursion formulae from the WittenKontsevich theorem as well as asymptotics of solutions to the first Painlevé equation. We also raise a conjecture on large genus asymptotics for n-point functions of ψ classes and partially verify the positivity of coefficients in generalized Mirzakhani’s formula of higher Weil-Petersson volumes.