Initial degenerations of Grassmannians

We construct closed immersions from initial degenerations of $${{\,\mathrm{Gr}\,}}_{0}(d,n)$$ —the open cell in the Grassmannian $${{\,\mathrm{Gr}\,}}(d,n)$$ given by nonvanishing all Plücker coordinates—to limits thin Schubert cells associated to diagrams induced face poset corresponding tropical linear space. These are isomorphisms when (d, n) equals (2, n), (3, 6) and 7). As an application we prove $${{\,\mathrm{Gr}\,}}_0(3,7)$$ is schön, Chow quotient $${{\,\mathrm{Gr}\,}}(3,7)$$ maximal torus $$ {\text {PGL}}(7)$$ log canonical compactification moduli space 7 points $${\mathbb {P}}^2$$ general position, making progress on a conjecture Hacking, Keel, Tevelev.