Blower, Gordon (2003) *Gaussian isoperimetric inequalities and transportation.* Positivity, 7 (3). pp. 203-224. ISSN 1385-1292

## 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.

Item Type: | Article |
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Journal or Publication Title: | Positivity |

Additional Information: | RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics |

Uncontrolled Keywords: | isoperimetric function - transportation - logarithmic Sobolev inequality - Orlicz spaces |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 2369 |

Deposited By: | ep_importer |

Deposited On: | 01 Apr 2008 15:26 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 07 Jan 2015 13:48 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/2369 |

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