Vania Mascioni

On the probability that finite spaces with random distances are metric spaces

For a set of 3 or 4 points we compute the exact probability that, after assigning the distances between these points uniformly at random from the set {1,...,n}, the space obtained is metric. The corresponding results for random real distances follow easily. We also prove estimates for the general case of a finite set of points with uniformly random real distances.

On Optimal Lattice Decompositions

A lattice decomposition lemma by H. Rosenthal is given an optimal refinement, both in the real and in the complex valued setting.