Recursions and asymptotics of intersection numbers (Q2822022)

Integrals of psi classes over moduli spaces of curves with marked points arise naturally in the asymptotics of Wei-Petersson volumes, Hurwitz numbers, Gromov-Witten invariants, graph enumerations and 2D gravity. This paper studies asymptotic expansions of such integrals by using cut-and-join type recursion formula from Witten-Kontsevich theorem and asymptotics of solutions to the first Painleve equation. The authors also raise a conjecture on large genus asymptotics of n-point functions of psi classes and partially verify the positivity of coefficients in generalized Mirzakhani's formula of higher Weil-Petersson volumes.