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In this paper, we explore some links between transforms derived by Stein'smethod and concentration inequalities. In particular, we show that thestochastic domination of the zero bias transform of a random variable isequivalent to sub-Gaussian concentration. For this purpose a new stochasticorder is considered. In a second time, we study the case of functions ofslightly dependent light-tailed random variables. We are able to recover thefamous McDiarmid type of concentration inequality for functions with thebounded difference property. Additionally, we obtain new concentration boundswhen we authorize a light dependence between the random variables. Finally, wegive a analogous result for another type of Stein's transform, the so-calledsize bias transform.

On the links between Stein transforms and concentration inequalities for dependent random variables