On nearly radial marginals of high-dimensional probability measures

Bo'Az Klartag

doi:10.4171/JEMS/213

On nearly radial marginals of high-dimensional probability measures

Bo'Az Klartag

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	723-754
Number of pages	32
Journal	Journal of the European Mathematical Society
Volume	12
Issue number	3
DOIs	https://doi.org/10.4171/JEMS/213
State	Published - 2010

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On nearly radial marginals of high-dimensional probability measures

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