  The purpose of this note is to show how simple Optimal Transport arguments,
on the real line, can be used in Superconcentration theory. This methodology is
efficient to produce sharp non-asymptotic variance bounds for various
functionals (maximum, median, $l^p$ norms) of standard Gaussian random vectors
in $\R^n$. The flexibility of this approach can also provide exponential
deviation inequalities reflecting preceding variance bounds. As a further
illustration, usual laws from Extreme theory and Coulomb gases are studied.
