Equivalence of the Poincar\'e inequality with a transport-chi-square   inequality in dimension one
  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. 
Benjamin Jourdain (CERMICS)
math.PR