  In this paper, we explore some links between transforms derived by Stein's
method and concentration inequalities. In particular, we show that the
stochastic domination of the zero bias transform of a random variable is
equivalent to sub-Gaussian concentration. For this purpose a new stochastic
order is considered. In a second time, we study the case of functions of
slightly dependent light-tailed random variables. We are able to recover the
famous McDiarmid type of concentration inequality for functions with the
bounded difference property. Additionally, we obtain new concentration bounds
when we authorize a light dependence between the random variables. Finally, we
give a analogous result for another type of Stein's transform, the so-called
size bias transform.
