Variance of Lipschitz functions and an isoperimetric problem for a class of product measures

Sergei G. Bobkov; Christian Houdré

doi:10.3150/bj/1178291721

Variance of Lipschitz functions and an isoperimetric problem for a class of product measures

Sergei G. Bobkov
, Christian Houdré

School of Mathematics

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

7 Scopus citations

Abstract

The maximal variance of Lipschitz functions (with respect to the ℓ¹-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability measures with given variance.

Original language	English (US)
Pages (from-to)	249-255
Number of pages	7
Journal	Bernoulli
Volume	2
Issue number	3
DOIs	https://doi.org/10.3150/bj/1178291721
State	Published - Jan 1 1996

Keywords

Isoperimetry
Lipschitz function
Variance inequality

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10.3150/bj/1178291721

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title = "Variance of Lipschitz functions and an isoperimetric problem for a class of product measures",

abstract = "The maximal variance of Lipschitz functions (with respect to the ℓ1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability measures with given variance.",

keywords = "Isoperimetry, Lipschitz function, Variance inequality",

author = "Bobkov, \{Sergei G.\} and Christian Houdr{\'e}",

year = "1996",

month = jan,

day = "1",

doi = "10.3150/bj/1178291721",

language = "English (US)",

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journal = "Bernoulli",

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publisher = "Bernoulli Society for Mathematical Statistics and Probability",

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T1 - Variance of Lipschitz functions and an isoperimetric problem for a class of product measures

AU - Bobkov, Sergei G.

AU - Houdré, Christian

PY - 1996/1/1

Y1 - 1996/1/1

N2 - The maximal variance of Lipschitz functions (with respect to the ℓ1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability measures with given variance.

AB - The maximal variance of Lipschitz functions (with respect to the ℓ1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability measures with given variance.

KW - Isoperimetry

KW - Lipschitz function

KW - Variance inequality

UR - https://www.scopus.com/pages/publications/0002215953

UR - https://www.scopus.com/pages/publications/0002215953#tab=citedBy

U2 - 10.3150/bj/1178291721

DO - 10.3150/bj/1178291721

M3 - Article

AN - SCOPUS:0002215953

SN - 1350-7265

VL - 2

SP - 249

EP - 255

JO - Bernoulli

JF - Bernoulli

IS - 3

ER -

Variance of Lipschitz functions and an isoperimetric problem for a class of product measures

Abstract

Keywords

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