On Measure Concentration of Vector-Valued Maps

• Autorzy: Michel Ledoux , Krzysztof Oleszkiewicz
• Języki publikacji: EN

Abstrakty

EN

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 $ℝ^{k}$. 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.

Kategorie tematyczne

• 60E15: Inequalities; stochastic orderings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: 55
• Numer: 3
• Strony: 261-278

Daty

wydano

2007

Twórcy

autor

Michel Ledoux

• Institut de Mathématiques, Université Paul-Sabatier, 31062 Toulouse, France

autor

Krzysztof Oleszkiewicz

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba55-3-7