Asymptotic volume formula for strata of Abelian differentials

Let $m=(m_1,\dots,m_n)$ be an unordered partition of $2g-2$, with $|m|=m_1+\dots+m_n=2g-2$, and let $\Pi_{2g-2}$ denote the set of all such partitions. Write $\operatorname{Vol}{\mathcal H}_1(m_1,\dots,m_n)$ for the volume of the stratum of unit-area Abelian differentials, and let $\varepsilon_1(m)$ denote the error term.

Asymptotic volume conjecture. For any $m\in\Pi_{2g-2}$,

$$\operatorname{Vol}{\mathcal H}_1(m_1,\dots,m_n)=\cfrac{4}{(m_1+1)\cdot\dots\cdot(m_n+1)}\cdot(1+\varepsilon_1(m)),$$

where

$$\lim_{g\to\infty}\max_{m\in\Pi_{2g-2}}|\varepsilon_1(m)|=0.$$

This gives a uniform large-genus asymptotic for the volumes of all strata. The source notes that the formula was known in the principal stratum at the time, while the corresponding statement for general strata remained open.