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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-3,
author = {F. Barthe and D. Cordero-Erausquin and M. Fradelizi},
title = {Shift inequalities of Gaussian type and norms of barycentres},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {245-259},
zbl = {0984.60024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-3}
}
F. Barthe; D. Cordero-Erausquin; M. Fradelizi. Shift inequalities of Gaussian type and norms of barycentres. Studia Mathematica, Tome 147 (2001) pp. 245-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-3/