Characterization of Gaussian measures by the isoperimetric property of half-spaces

S. G. Bobkov; C. Houdré

doi:10.1007/BF02364810

Characterization of Gaussian measures by the isoperimetric property of half-spaces

S. G. Bobkov
, C. Houdré

School of Mathematics

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

2 Scopus citations

Abstract

If the half-spaces of the form {x ∈ Rⁿ : x₁ ≤ c} are extremal in the isoperimetric problem for a product-measure μⁿ, n ≥ 2, then the marginal distribution of μ is Gaussian.

Original language	English (US)
Pages (from-to)	270-275
Number of pages	6
Journal	Journal of Mathematical Sciences (United States)
Volume	93
Issue number	3
DOIs	https://doi.org/10.1007/BF02364810
State	Published - 1999

Bibliographical note

Funding Information:
This research was partially supported by the International Science Foundation, grant NXZ000-NXZ300, and by the Russian State Committee for Higher Education, grant 94-1.4-57. The research was also partially supported by an NSF Postdoctoral Fellowship. The second author enjoyed the hospitality of the Steklov Mathematical Institute (St. Petersburg Branch) and of the Department of Mathematics, University of Syktyvkar, Russia, where part of this research was done.

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title = "Characterization of Gaussian measures by the isoperimetric property of half-spaces",

abstract = "If the half-spaces of the form \{x ∈ Rn : x1 ≤ c\} are extremal in the isoperimetric problem for a product-measure μn, n ≥ 2, then the marginal distribution of μ is Gaussian.",

author = "Bobkov, \{S. G.\} and C. Houdr{\'e}",

note = "Funding Information: This research was partially supported by the International Science Foundation, grant NXZ000-NXZ300, and by the Russian State Committee for Higher Education, grant 94-1.4-57. The research was also partially supported by an NSF Postdoctoral Fellowship. The second author enjoyed the hospitality of the Steklov Mathematical Institute (St. Petersburg Branch) and of the Department of Mathematics, University of Syktyvkar, Russia, where part of this research was done.",

year = "1999",

doi = "10.1007/BF02364810",

language = "English (US)",

volume = "93",

pages = "270--275",

journal = "Journal of Mathematical Sciences (United States)",

issn = "1072-3374",

publisher = "Springer",

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TY - JOUR

T1 - Characterization of Gaussian measures by the isoperimetric property of half-spaces

AU - Bobkov, S. G.

AU - Houdré, C.

N1 - Funding Information: This research was partially supported by the International Science Foundation, grant NXZ000-NXZ300, and by the Russian State Committee for Higher Education, grant 94-1.4-57. The research was also partially supported by an NSF Postdoctoral Fellowship. The second author enjoyed the hospitality of the Steklov Mathematical Institute (St. Petersburg Branch) and of the Department of Mathematics, University of Syktyvkar, Russia, where part of this research was done.

PY - 1999

Y1 - 1999

N2 - If the half-spaces of the form {x ∈ Rn : x1 ≤ c} are extremal in the isoperimetric problem for a product-measure μn, n ≥ 2, then the marginal distribution of μ is Gaussian.

AB - If the half-spaces of the form {x ∈ Rn : x1 ≤ c} are extremal in the isoperimetric problem for a product-measure μn, n ≥ 2, then the marginal distribution of μ is Gaussian.

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DO - 10.1007/BF02364810

M3 - Article

AN - SCOPUS:33847761564

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JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

IS - 3

ER -

Characterization of Gaussian measures by the isoperimetric property of half-spaces

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