The distributions of traffics are defined and are applied for families of larges random matrices, random groups and infinite random rooted graphs with uniformly bounded degree. There are constructed by adding axioms in Voiculescu’s definition of ∗-distribution of non commutative random variables. The convergence in distribution of traffics generalizes Benjamini, Schramm, Aldous, Lyons’ weak loc...

We characterize the k -torsion freeness of module differentials order n a point hypersurface in terms singular locus corresponding local ring.