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.

翻译：在本文中,我们探索了斯坦因方法产生的变异与集中不平等之间的某些联系。 特别是, 我们显示随机变异零偏移的随机变异的随机偏移的随机偏移主导性与亚高加索的浓度相当。 为此考虑一个新的随机变异顺序。 我们第二次研究轻微依赖的轻尾随机变异的功能。 我们能够恢复著名的McDiarmid型的与封闭差异属性函数的集中不平等。 此外, 当我们批准随机变异之间的轻依赖性时, 我们获得了新的集中界限。 最后, 我们给另一种类型的斯坦变异, 即所谓的大小偏差, 提供了类似的结果 。