in this talk, we present some results originating from a new general inequality obtained by combining the chen–stein method with malliavin calculus on the poisson space, such as multidimensional poisson approximations, mixed limit theorems, as well as a characterization of asymptotic independence for u–statistics. applications to stochastic geometry through limit theorems involving the joint convergence of vectors of subgraph–counting statistics exhibiting both a poisson and a gaussian behavior will also be discussed.