Electronic Communications in Probability

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

Benjamin Jourdain

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263176

Digital Object Identifier
doi:10.1214/ECP.v17-2115

Mathematical Reviews number (MathSciNet)
MR2981899

Zentralblatt MATH identifier
1253.26031

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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References

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