The surface measure and cone measure on the sphere of ℓ np

Assaf Naor

doi:10.1090/S0002-9947-06-03939-0

The surface measure and cone measure on the sphere of ℓ ⁿ_p

Assaf Naor

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

85 Scopus citations

Abstract

We prove a concentration inequality for the ⁿ_p norm on the ⁿ_psphere for p, q > 0. This inequality, which generalizes results of Schechtman and Zinn (2000), is used to study the distance between the cone measure and surface measure on the sphere of ⁿ _p. In particular, we obtain a significant strengthening of the inequality derived by Naor and Romik (2003), and calculate the precise dependence of the constants that appeared there on p.

Original language	English (US)
Pages (from-to)	1045-1079
Number of pages	35
Journal	Transactions of the American Mathematical Society
Volume	359
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9947-06-03939-0
State	Published - Mar 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Concentration inequalities
Cone measure
Convex geometry.
Geometry of
Surface measure

Access to Document

10.1090/S0002-9947-06-03939-0

Cite this

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AB - We prove a concentration inequality for the np norm on the npsphere for p, q > 0. This inequality, which generalizes results of Schechtman and Zinn (2000), is used to study the distance between the cone measure and surface measure on the sphere of n p. In particular, we obtain a significant strengthening of the inequality derived by Naor and Romik (2003), and calculate the precise dependence of the constants that appeared there on p.

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KW - Cone measure

KW - Convex geometry.

KW - Geometry of

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