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

Random fusion frames are nearly equiangular and tight