Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 09/2003 |
---|---|

<mark>Journal</mark> | Positivity |

Issue number | 3 |

Volume | 7 |

Number of pages | 22 |

Pages (from-to) | 203-224 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics