PUB - Publikationen an der Universität Bielefeld

We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d - 1 for any d is an element of N. The bounds are based on dth order derivatives or difference operators. In particular, we consider deviations of functions of independent random variables and differentiable functions over probability measures satisfying a logarithmic Sobolev inequality, and functions on the unit sphere. Applications include concentration inequalities for U-statistics as well as for classes of symmetric functions via polynomial approximations on the sphere (Edgeworth-type expansions).