Poincaré inequalities and dimension free concentration of measure

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Applications of Stein's method for concentration inequalities (2009, background): “Also in [5, 21, 22], the authors deal with tails (possibly) larger than Gaussian.”
A characterization of dimension free concentration in terms of transportation inequalities (2008, background): “On R , a relatively weak sufficient condition for T2 (and other transportationcost inequalities) has been established by the author in [21] (Theorem 4.”
Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry (2010, methodology): “One is based on the Lyapunov function approach [4; 30; 3], the other is based on mass transportation method [35; 36] (see also [15; 54; 20; 22]).”