On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag

Journal of the European Mathematical Society (2010)

  • Volume: 012, Issue: 3, page 723-754
  • ISSN: 1435-9855

Abstract

top
Suppose that μ is an absolutely continuous probability measure on R n, for large n . Then μ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if n ( C / ε ) C d , then there exist d -dimensional marginals of μ that are ε -far from being sphericallysymmetric, in an appropriate sense. Here C > 0 is a universal constant.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.