Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension

S. Sodin

doi:10.1007/978-3-540-72053-9_16

Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension

S. Sodin^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

16 Scopus citations

Abstract

If the Euclidean norm | · | is strongly concentrated with respect to a measure μ, the average distribution of an average marginal of μ has Gaussian asymptotics that captures tail behaviour. If the marginals of μ have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show applications to measures of geometric origin.

Original language	English
Title of host publication	Geometric Aspects of Functional Analysis
Subtitle of host publication	Israel Seminar 2004-2005
Publisher	Springer Verlag
Pages	271-295
Number of pages	25
ISBN (Print)	3540720529, 9783540720522
DOIs	https://doi.org/10.1007/978-3-540-72053-9_16
State	Published - 2007
Externally published	Yes

Publication series

Name	Lecture Notes in Mathematics
Volume	1910
ISSN (Print)	0075-8434

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10.1007/978-3-540-72053-9_16

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AB - If the Euclidean norm | · | is strongly concentrated with respect to a measure μ, the average distribution of an average marginal of μ has Gaussian asymptotics that captures tail behaviour. If the marginals of μ have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show applications to measures of geometric origin.

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Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension

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