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We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1.
Rockafellar, R. T. (1970). Convex Analysis
1970
Earlier work this paper cites.
Ajtai , M., Komlós , J. and Tusnády , G. (1984). On optimal matchings. Combinatorica
1984
Earlier work this paper cites.
Evans, L. C. and Gariepy, R. F. (1992). Measure Theory and Fine Properties of Functions
1992
Earlier work this paper cites.
Talagrand, M. (1992). Matching random samples in many dimensions. Ann. Appl. Probab
1992
Earlier work this paper cites.
Talagrand , M. and Yukich , J. E. (1993). The integrability of the square exponential transportation cost. Ann. Appl. Probab
1993
Earlier work this paper cites.
Talagrand , M. (1994). The transportation cost from the uniform measure to the empirical measure in dimension ≥ 3 \geq 3 . Ann. Probab
1994
Earlier work this paper cites.
Dobrić, V. and Yukich , J. E. (1995). Asymptotics for transportation cost in high dimensions. J. Theoret. Probab
1995
Earlier work this paper cites.
Gangbo, W. and McCann, R. J. (1996). The Geometry of Optimal Transportation. Acta Math
1996
Earlier work this paper cites.
Heinich, H., and Lootgieter, J. C. (1996). Convergence des fonctions monotones. Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 322(9), 869-874
1996
Cited alongside, same era.
Cuesta-Albertos, J.A., Matrán, C. and Tuero-Díaz, A. (1997). Optimal transportation plans and convergence in distribution. J. Multivariate Analysis
1997
Cited alongside, same era.
Rachev , S. T. and Rüschendorf , L. (1998). Mass Transportation Problems. (2 Vols)
1998
Cited alongside, same era.
Rockafellar, R. T. and Wets, R. J. (1998). Variational Analysis
1998
Cited alongside, same era.
del Barrio, E., Matrán, C. and Giné, E. (1999). Central limit theorems for the Wasserstein distance between the empirical and the true distribution. Ann. Probab
1999
Cited alongside, same era.
del Barrio, E. and Matrán, C. (2013). Rates of convergence for partial mass problems. Probab. Theory Relat. Fields
2013
Later among the works it cites.
Boucheron, S., Lugosi, G. and Massart, P. (2013). Concentration Inequalities. A Nonasymptotic Theory of Independence
2013
Later among the works it cites.
Fournier, N. and Guillin, A. (2015). On the rate of convergence in Wasserstein distance of the empirical measure, Probability Theory and Related Fields
2015
Later among the works it cites.
2016
Later among the works it cites.
Bobkov, S. and Ledoux, M. (2016). One-dimensional empirical measures, order statistics and Kantorovich transport distances. To appear in Memoirs of the AMS
2016
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Villani, C. (2003). Topics in Optimal Transportation
2003
Cited alongside, same era.
del Barrio, E., Giné, E. and Utzet, F. (2005). Asymptotics for L 2 L_{2} functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances. Bernoulli
2005
Cited alongside, same era.
2009
Cited alongside, same era.
Later among the works it cites.
Rippl, T., Munk, A. and Sturm, A. (2016). Limit laws of the empirical Wasserstein distance: Gaussian distributions. J. of Multivariate Analysis
2016
Later among the works it cites.
2016
Later among the works it cites.