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 on the sphere
Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses
Logarithmic Sobolev Inequalities for Inhomogeneous Markov Semigroups
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