Georgia Institute of Technology College of Sciences

We develop an extension of the Stein-Malliavin calculus which allows to measure the Wasserstein distance between the probability distributions of $ (X, Y)$ and $(Z,Y)$, where $X,Y$ are arbitrary random vectors and $ Z\sim N(0, \sigma ^{2})$ is independent of $Y$. In particular, this method allows to quantify the asymptotic independence between sequences of random variables and vectors. We will discuss some particular applications of this method to various limit theorems.