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Let   $S_g$   be a closed surface of genus   $g$   and   $\mathbb{M}_g$   be the moduli space of   $S_g$   endowed with the Weil–Petersson metric. In this article we investigate the Weil–Petersson curvatures of   $\mathbb{M}_g$   for large genus   $g$  . First, we study the asymptotic behavior of the extremal Weil–Petersson holomorphic sectional curvatures at certain thick surfaces in   $\mathbb{M}_g$   as   $g \to \infty$  . Then we prove two curvature properties on the whole space   $\mathbb{M}_g$   as   $g\to \infty$   in a probabilistic way.

On the Weil–Petersson Curvature of the Moduli Space of Riemann Surfaces of Large Genus