On nearly radial marginals of high-dimensional probability measures

Klartag, Bo'az. "On nearly radial marginals of high-dimensional probability measures." Journal of the European Mathematical Society 012.3 (2010): 723-754. <http://eudml.org/doc/277460>.

@article{Klartag2010,
abstract = {Suppose that $\mu $ is an absolutely continuous probability measure on $\mathbb \{^\}R$n, for large $n$. Then $\mu $ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if $n\ge (C/\varepsilon )^\{Cd\}$, then there exist $d$-dimensional marginals of $\mu $ that are $\varepsilon $-far from being sphericallysymmetric, in an appropriate sense. Here $C>0$ is a universal constant.},
author = {Klartag, Bo'az},
journal = {Journal of the European Mathematical Society},
keywords = {high-dimensional measures; marginals; Dvoretzky's theorem; high-dimensional measures; Dvoretzky's theorem; spherically-symmetric; radially-symmetric.},
language = {eng},
number = {3},
pages = {723-754},
publisher = {European Mathematical Society Publishing House},
title = {On nearly radial marginals of high-dimensional probability measures},
url = {http://eudml.org/doc/277460},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Klartag, Bo'az
TI - On nearly radial marginals of high-dimensional probability measures
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 3
SP - 723
EP - 754
AB - Suppose that $\mu $ is an absolutely continuous probability measure on $\mathbb {^}R$n, for large $n$. Then $\mu $ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if $n\ge (C/\varepsilon )^{Cd}$, then there exist $d$-dimensional marginals of $\mu $ that are $\varepsilon $-far from being sphericallysymmetric, in an appropriate sense. Here $C>0$ is a universal constant.
LA - eng
KW - high-dimensional measures; marginals; Dvoretzky's theorem; high-dimensional measures; Dvoretzky's theorem; spherically-symmetric; radially-symmetric.
UR - http://eudml.org/doc/277460
ER -