Uniform large-genus asymptotics of Weil-Petersson volumes

Let Vg,n denote the Weil--Petersson volume of the moduli space of genus-g hyperbolic surfaces with n cusps. We obtain an asymptotic expansion in inverse powers of the genus as g→∞, uniformly for all n≥0. This includes cusp counts of order √ g and larger, where the fixed-n expansion of Mirzakhani and Zograf no longer gives a uniform approximation. The leading term is explicit and has relative error O(g⁻¹). Truncating the expansion at a suitably chosen order proportional to √ g gives relative error O(exp(-a√ g)) for some $a>0$, with no restriction on the growth of n. For fixed n, the leading term identifies the universal constant in the Mirzakhani--Zograf asymptotics as 1/√π, as conjectured by Zograf. We also answer two questions of Mirzakhani: we determine explicit asymptotic profiles for volume ratios uniformly in the number of cusps, and for adjacent coefficient ratios of the one-boundary volume polynomial uniformly over all degrees. The proof uses a positive recursion for mixed κ₁--$ψ$ intersection numbers, with the absolute normalization determined by comparison with the known asymptotics of pure $ψ$ intersection numbers.