Intermediate complex structure limit for Calabi-Yau metrics

We study polarised degenerations of $n$-dimensional Calabi-Yau hypersurfaces $\{F_0{F}_1\dots F_m+tF=0\}$, where the essential skeleton has dimension $1\le m\le n-1$. 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.