Shift inequalities of Gaussian type and norms of barycentres
Volume 146 / 2001
Studia Mathematica 146 (2001), 245-259
MSC: 28A75, 26B15, 26D10, 52A40.
DOI: 10.4064/sm146-3-3
Abstract
We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.
