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Gaussian isoperimetric inequalities and transportation.

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Gaussian isoperimetric inequalities and transportation. / Blower, Gordon.
In: Positivity, Vol. 7, No. 3, 09.2003, p. 203-224.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Blower, G 2003, 'Gaussian isoperimetric inequalities and transportation.', Positivity, vol. 7, no. 3, pp. 203-224. https://doi.org/10.1023/A:1026242611940

APA

Blower, G. (2003). Gaussian isoperimetric inequalities and transportation. Positivity, 7(3), 203-224. https://doi.org/10.1023/A:1026242611940

Vancouver

Blower G. Gaussian isoperimetric inequalities and transportation. Positivity. 2003 Sept;7(3):203-224. doi: 10.1023/A:1026242611940

Author

Blower, Gordon. / Gaussian isoperimetric inequalities and transportation. In: Positivity. 2003 ; Vol. 7, No. 3. pp. 203-224.

Bibtex

@article{7fdff9dd27f44b3d871b98e70f6632c1,
title = "Gaussian isoperimetric inequalities and transportation.",
abstract = "Any probability measure on d which satisfies the Gaussian or exponential isoperimetric inequality fulfils a transportation inequality for a suitable cost function. Suppose that W (x) dx satisfies the Gaussian isoperimetric inequality: then a probability density function f with respect to W (x) dx has finite entropy, provided that t . This strengthens the quadratic logarithmic Sobolev inequality of Gross (Amr. J. Math 97 (1975) 1061). Let (dx) = e –(x) dx be a probability measure on d, where is uniformly convex. Talagrand's technique extends to monotone rearrangements in several dimensions (Talagrand, Geometric Funct. Anal. 6 (1996) 587), yielding a direct proof that satisfies a quadratic transportation inequality. The class of probability measures that satisfy a quadratic transportation inequality is stable under multiplication by logarithmically bounded Lipschitz densities.",
keywords = "isoperimetric function - transportation - logarithmic Sobolev inequality - Orlicz spaces",
author = "Gordon Blower",
note = "RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics",
year = "2003",
month = sep,
doi = "10.1023/A:1026242611940",
language = "English",
volume = "7",
pages = "203--224",
journal = "Positivity",
issn = "1385-1292",
publisher = "Birkhauser Verlag Basel",
number = "3",

}

RIS

TY - JOUR

T1 - Gaussian isoperimetric inequalities and transportation.

AU - Blower, Gordon

N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics

PY - 2003/9

Y1 - 2003/9

N2 - Any probability measure on d which satisfies the Gaussian or exponential isoperimetric inequality fulfils a transportation inequality for a suitable cost function. Suppose that W (x) dx satisfies the Gaussian isoperimetric inequality: then a probability density function f with respect to W (x) dx has finite entropy, provided that t . This strengthens the quadratic logarithmic Sobolev inequality of Gross (Amr. J. Math 97 (1975) 1061). Let (dx) = e –(x) dx be a probability measure on d, where is uniformly convex. Talagrand's technique extends to monotone rearrangements in several dimensions (Talagrand, Geometric Funct. Anal. 6 (1996) 587), yielding a direct proof that satisfies a quadratic transportation inequality. The class of probability measures that satisfy a quadratic transportation inequality is stable under multiplication by logarithmically bounded Lipschitz densities.

AB - Any probability measure on d which satisfies the Gaussian or exponential isoperimetric inequality fulfils a transportation inequality for a suitable cost function. Suppose that W (x) dx satisfies the Gaussian isoperimetric inequality: then a probability density function f with respect to W (x) dx has finite entropy, provided that t . This strengthens the quadratic logarithmic Sobolev inequality of Gross (Amr. J. Math 97 (1975) 1061). Let (dx) = e –(x) dx be a probability measure on d, where is uniformly convex. Talagrand's technique extends to monotone rearrangements in several dimensions (Talagrand, Geometric Funct. Anal. 6 (1996) 587), yielding a direct proof that satisfies a quadratic transportation inequality. The class of probability measures that satisfy a quadratic transportation inequality is stable under multiplication by logarithmically bounded Lipschitz densities.

KW - isoperimetric function - transportation - logarithmic Sobolev inequality - Orlicz spaces

U2 - 10.1023/A:1026242611940

DO - 10.1023/A:1026242611940

M3 - Journal article

VL - 7

SP - 203

EP - 224

JO - Positivity

JF - Positivity

SN - 1385-1292

IS - 3

ER -