The Weil-Petersson diameter of moduli space for large genus

We determine the large-genus order of the Weil-Petersson diameter of ${\mathcal{M}}_{g,n}$ for each fixed number of punctures: namely, $\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}({\mathcal{M}}_{g,n})\asymp \sqrt{g}\log g$. The main new ingredient is an integrated Ricci estimate for geodesics that minimize in moduli space and have thick endpoints, with no systole bound along their interiors.