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

Benjamin Jourdain (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHRISK - Mathematical Risk handling

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.

Domaines: Probabilités [math.PR]

Benjamin Jourdain. Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one. 2012. ⟨hal-00711885⟩