  This paper demonstrates that random, independently chosen equi-dimensional
subspaces with a unitarily invariant distribution in a real Hilbert space
provide nearly tight, nearly equiangular fusion frames. The angle between a
pair of subspaces is measured in terms of the Hilbert-Schmidt inner product of
the corresponding orthogonal projections. If the subspaces are selected at
random, then a measure concentration argument shows that these inner products
concentrate near an average value. Overwhelming success probability for near
tightness and equiangularity is guaranteed if the dimension of the subspaces is
sufficiently small compared to that of the Hilbert space and if the dimension
of the Hilbert space is small compared to the sum of all subspace dimensions.
