Electronic Communications in Probability

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

Benjamin Jourdain

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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.<br /><br />

Article information

Electron. Commun. Probab., Volume 17 (2012), paper no. 43, 12 pp.

Accepted: 26 September 2012
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 60E15: Inequalities; stochastic orderings

Poincaré inequality transport inequality chi-square pseudo-distance Wasserstein distance

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Jourdain, Benjamin. Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one. Electron. Commun. Probab. 17 (2012), paper no. 43, 12 pp. doi:10.1214/ECP.v17-2115. https://projecteuclid.org/euclid.ecp/1465263176

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