Geodesic
On Measure Concentration of Vector-Valued Maps
Michel Ledoux 1   ; Krzysztof Oleszkiewicz 2
1 Institut de Mathématiques Université Paul-Sabatier 31062 Toulouse, France
2 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 3, pp. 261-278 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\mathbb R^{k}$. 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.
DOI : 10.4064/ba55-3-7
Keywords: study concentration properties vector valued maps particular describe inequalities which capture exact dimensional behavior lipschitz maps values mathbb end study particular domination principle projections which might independent interest further compare conclusions earlier results pinelis gaussian discuss extensions infinite dimensional setting

Michel Ledoux  1   ; Krzysztof Oleszkiewicz  2

1 Institut de Mathématiques Université Paul-Sabatier 31062 Toulouse, France
2 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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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) no. 3, pp. 261-278. doi: 10.4064/ba55-3-7

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