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

   
@article{ECP2115,
	author = {Benjamin Jourdain},
	title = {Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {Poincaré inequality; transport inequality; chi-square pseudo-distance; Wasserstein distance},
	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.

},
	pages = {no. 43, 1-12},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-2115},    
        url = {http://ecp.ejpecp.org/article/view/2115}}