We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and second order derivatives. Applications to functions on the discrete cube and stochastic Hoeffding type expansions in mathematical statistics are studied as well as linear eigenvalue statistics in random matrix theory.
"Second order concentration via logarithmic Sobolev inequalities." Bernoulli 26 (1) 93 - 126, February 2020. https://doi.org/10.3150/19-BEJ1118