Characterization of Gaussian measures by the isoperimetric property of half-spaces
type: Item
instance of: scholarly article
title: Characterization of Gaussian measures by the isoperimetric property of half-spaces
zbMATH Open document ID: 0924.60009
DOI: 10.1007/BF02364810
author: Christian Houdré
author: S. G. Bobkov
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-07-13T00:00:00Z
review text: Let \(\mu\) be a probability measure on the real line \(R\), and let \(\mu^n\) be its \(n\)th power on \(R^n\). Let \(A^h\) be the open \(h\)-neighborhood, \(h>0\), of the subset \(A\subset R^n\) in the sense of Euclidean distance. The authors prove that for \(n\geq 2\), if for all \(p\in (0,1)\) and all \(h>0\) the minimal value of \(\mu^n(A^h)\) is attained at a standard half-space, then \(\mu\) is Gaussian, possibly degenerate. The hypotheses of this result can be weakened if in addition \(\mu\) is symmetric and has a finite second moment.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 1300647
zbMATH Keywords: Gaussian measure
zbMATH Keywords: isoperimetric inequality
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
cites work: Extremal properties of half-spaces for log-concave distributions
cites work: Symétrisation dans l'espace de Gauss.
cites work: Q5623005
cites work: Concentration of measure and isoperimetric inequalities in product spaces
full work available at URL: https://doi.org/10.1007/bf02364810
OpenAlex ID: W1968899263
description: scientific article; zbMATH DE number 1300647