Equivalence of the Poincar\'e inequality with a transport-chi-square inequality in dimension one
classification
🧮 math.PR
keywords
inequalitytransport-chi-squaredimensionpoincarcheckchi-squaredistanceequivalence
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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.
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