  Starting from concentration of measure hypotheses on $m$ random vectors
$Z_1,\ldots, Z_m$, this article provides an expression of the concentration of
functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each
variable depend on the product of the norms (or semi-norms) of the other
variables (as if $\phi$ were a product). We illustrate the importance of this
result through various generalizations of the Hanson-Wright concentration
inequality as well as through a study of the random matrix $XDX^T$ and its
resolvent $Q = (I_p - \frac{1}{n}XDX^T)^{-1}$, where $X$ and $D$ are random,
which have fundamental interest in statistical machine learning applications.

Probability;Machine Learning