Recursions and asymptotics of intersection numbers

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