On Measure Concentration of Vector-Valued Maps
Michel Ledoux ; Krzysztof Oleszkiewicz
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007), p. 261-278 / Harvested from The Polish Digital Mathematics Library
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We study concentration properties for vector-valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in ℝk. To this end, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions with earlier results by Pinelis in the Gaussian case, and discuss extensions to the infinite-dimensional setting.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:281339 
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Michel Ledoux; Krzysztof Oleszkiewicz. On Measure Concentration of Vector-Valued Maps. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 261-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-3-7/