A central limit theorem for projections of the cube
  We prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case is with respect to the Haar measure on the Grassmannian manifold. 
Grigoris Paouris, Peter Pivovarov and Joel Zinn
math.PR math.MG