Centroid bodies and the logarithmic Laplace transform - A unified approach

Bo'az Klartag; Emanuel Milman

doi:10.1016/j.jfa.2011.09.003

Centroid bodies and the logarithmic Laplace transform - A unified approach

Bo'az Klartag, Emanuel Milman

Technion - Israel Institute of Technology, Tel Aviv University

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

Abstract

We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's psi(2) constant is obtained. Along the way, we present some new bounds on the volume of L-p-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the Lp-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author. (C) 2011 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	10-34
Number of pages	25
Journal	Journal of Functional Analysis
Volume	262
Issue number	1
Early online date	23 Sep 2011
DOIs	https://doi.org/10.1016/j.jfa.2011.09.003
State	Published - 1 Jan 2012

Keywords

Hyperplane conjecture
Logarithmic Laplace transform
Psi-2

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2011.09.003

http://arxiv.org/abs/1103.2985License: Other

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abstract = "We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's psi(2) constant is obtained. Along the way, we present some new bounds on the volume of L-p-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the Lp-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author. (C) 2011 Elsevier Inc. All rights reserved.",

keywords = "Hyperplane conjecture, Logarithmic Laplace transform, Psi-2",

author = "Bo'az Klartag and Emanuel Milman",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (B. Klartag), [email protected] (E. Milman). 1 Supported in part by the Israel Science Foundation and by a Marie Curie Reintegration Grant from the Commission of the European Communities. 2 Supported by ISF, GIF and the Taub Foundation (Landau Fellow).",

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AB - We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's psi(2) constant is obtained. Along the way, we present some new bounds on the volume of L-p-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the Lp-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author. (C) 2011 Elsevier Inc. All rights reserved.

KW - Hyperplane conjecture

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DO - 10.1016/j.jfa.2011.09.003

M3 - مقالة

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EP - 34

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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ER -

Centroid bodies and the logarithmic Laplace transform - A unified approach

Abstract

Keywords

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