On Measure Concentration of Vector-Valued Maps

Michel Ledoux, and Krzysztof Oleszkiewicz. "On Measure Concentration of Vector-Valued Maps." Bulletin of the Polish Academy of Sciences. Mathematics 55.3 (2007): 261-278. <http://eudml.org/doc/281339>.

@article{MichelLedoux2007,
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 $ℝ^\{k\}$. 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.},
author = {Michel Ledoux, Krzysztof Oleszkiewicz},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {concentration of measure, vector-valued map, moment comparison, Gaussian measure},
language = {eng},
number = {3},
pages = {261-278},
title = {On Measure Concentration of Vector-Valued Maps},
url = {http://eudml.org/doc/281339},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Michel Ledoux
AU - Krzysztof Oleszkiewicz
TI - On Measure Concentration of Vector-Valued Maps
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 3
SP - 261
EP - 278
AB - 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.
LA - eng
KW - concentration of measure, vector-valued map, moment comparison, Gaussian measure
UR - http://eudml.org/doc/281339
ER -