2017/09/30 by Sergey G. Bobkov, Friedrich Götze, Holger Sambale · 1 citation
Mathematics · #math.PR #msc:41A10 #msc:41A80 #msc:60E15 #msc:60F10
paper · pdf · doi:10.1142/s0219199718500438
some new material and examples added
arxiv created 2018/08/13 · arxiv updated 2018/08/14
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d-1 for any d ∈ ℕ. The bounds are based on d-th 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).