TY - JOUR
T1 - Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one
AU - Jourdain, Benjamin
PY - 2012/10/10
Y1 - 2012/10/10
N2 - 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.
AB - 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.
KW - Chi-square pseudo-distance
KW - Poincaré inequality
KW - Transport inequality
KW - Wasserstein distance
UR - https://www.scopus.com/pages/publications/84867137856
U2 - 10.1214/ECP.v17-2115
DO - 10.1214/ECP.v17-2115
M3 - Article
AN - SCOPUS:84867137856
SN - 1083-589X
VL - 17
JO - Electronic Communications in Probability
JF - Electronic Communications in Probability
ER -