Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one

Benjamin Jourdain

doi:10.1214/ECP.v17-2115

Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one

Benjamin Jourdain

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

In this paper, we prove that, in dimension one, the Poincaré inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality.

langue originale	Anglais
journal	Electronic Communications in Probability
Volume	17
Les DOIs	https://doi.org/10.1214/ECP.v17-2115
état	Publié - 10 oct. 2012

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10.1214/ECP.v17-2115

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title = "Equivalence of the Poincar{\'e} inequality with a transport-chi-square inequality in dimension one",

abstract = "In this paper, we prove that, in dimension one, the Poincar{\'e} inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality.",

keywords = "Chi-square pseudo-distance, Poincar{\'e} inequality, Transport inequality, Wasserstein distance",

author = "Benjamin Jourdain",

year = "2012",

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AU - Jourdain, Benjamin

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AB - In this paper, we prove that, in dimension one, the Poincaré inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality.

KW - Chi-square pseudo-distance

KW - Poincaré inequality

KW - Transport inequality

KW - Wasserstein distance

UR - https://www.scopus.com/pages/publications/84867137856

U2 - 10.1214/ECP.v17-2115

DO - 10.1214/ECP.v17-2115

M3 - Article

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SN - 1083-589X

VL - 17

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

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Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one

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