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

Benjamin Jourdain (Université Paris-Est, CERMICS)

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.


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Pages: 1-12

Publication Date: September 26, 2012

DOI: 10.1214/ECP.v17-2115

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