Abstract
We establish the asymptotic expansion of certain integrals of [Formula: see text] classes on moduli spaces of curves [Formula: see text], when either the [Formula: see text] or [Formula: see text] 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 Painlevé equation. We also raise a conjecture on large genus asymptotics for [Formula: see text]-point functions of [Formula: see text] classes and partially verify the positivity of coefficients in generalized Mirzakhani’s formula of higher Weil–Petersson volumes.
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