On Measure Concentration of Vector-Valued Maps

Volume 55 / 2007

Michel Ledoux, Krzysztof Oleszkiewicz Bulletin Polish Acad. Sci. Math. 55 (2007), 261-278 MSC: Primary 60E15. DOI: 10.4064/ba55-3-7

Abstract

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.

Authors

  • Michel LedouxInstitut de Mathématiques
    Université Paul-Sabatier
    31062 Toulouse, France
    e-mail
  • Krzysztof OleszkiewiczInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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