Eskin–Zorich large-genus volume conjecture for strata of differentials

Let $g$ tend to infinity, let $\boldsymbol{\boldsymbol{k}}=(k_1,\ldots,k_n)$ be a partition of $2g-2$, and write ${\rm Vol}(k_1,\ldots,k_n)$ for the volume of the corresponding stratum. Define the error term $\epsilon_1(\mu)$ by the asserted asymptotic formula. Eskin–Zorich's volume conjecture. The volumes of strata satisfy

$${\rm Vol}(k_1,\ldots,k_n)=\frac{4}{(k_1+1)(k_2+1)\cdots(k_n+1)}(1+\epsilon_1(\mu)),$$

where

$$\lim_{g\to\infty}\left(\max_{\mu\vdash 2g-2}|\epsilon_1(\mu)|\right)=0.$$

This predicts a uniform large-genus asymptotic across all strata of Abelian differentials. The paper proves the corresponding asymptotic for the principal stratum and for the stratum with one zero, but the uniform statement for all strata remains open in the source.