  We study the high-dimensional limit of (projective) Stiefel and Grassmann
manifolds as metric measure spaces in Gromov's topology. The limits are either
the infinite-dimensional Gaussian space or its quotient by an mm-isomorphic
group action, which are drastically different from the manifolds. As a
corollary, we obtain some asymptotic estimates of the observable diameter of
(projective) Stiefel and Grassmann manifolds.
