Shift inequalities of Gaussian type and norms of barycentres
F. Barthe, D. Cordero-Erausquin, M. Fradelizi (2001)
Studia Mathematica
Similarity:
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. ...