A fast algorithm for generating a uniform distribution inside a   high-dimensional polytope
  We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its usage of pseudo-random source numbers, and present an interesting result on the correlation between the coordinates. 
A. van Hameren and R. Kleiss