Intermediate complex structure limit for Calabi-Yau metrics

We study polarised degenerations of $n$-dimensional Calabi-Yau hypersurfaces $\{ F_0F_1\ldots F_m+tF=0\}$, where the essential skeleton has dimension $1\leq m\leq n-1$. We will describe the limiting behaviour of the Calabi-Yau potential at the $C^0$-level, in terms of an optimal transport problem, and in terms of non-archimedean potential theory.