Convex bodies and norms associated to convex measures

Sergey G. Bobkov

doi:10.1007/s00440-009-0209-7

Convex bodies and norms associated to convex measures

Sergey G. Bobkov

School of Mathematics

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

28 Scopus citations

Abstract

Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.

Original language	English (US)
Pages (from-to)	303-332
Number of pages	30
Journal	Probability Theory and Related Fields
Volume	147
Issue number	1
DOIs	https://doi.org/10.1007/s00440-009-0209-7
State	Published - Feb 2010

Bibliographical note

Funding Information:
Supported in part by the NSF grant DMS-0706866.

Keywords

Convex measures
Floating bodies
Isotropic convex bodies

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10.1007/s00440-009-0209-7

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title = "Convex bodies and norms associated to convex measures",

abstract = "Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.",

keywords = "Convex measures, Floating bodies, Isotropic convex bodies",

author = "Bobkov, {Sergey G.}",

note = "Funding Information: Supported in part by the NSF grant DMS-0706866.",

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N2 - Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.

AB - Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.

KW - Convex measures

KW - Floating bodies

KW - Isotropic convex bodies

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JO - Probability Theory and Related Fields

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SN - 0178-8051

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Convex bodies and norms associated to convex measures

Abstract

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Keywords

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