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We compute exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete, or semi-discrete, setting.
E. Schrödinger, “Über die Umkehrung der Naturgesetze.”
1931
Earlier work this paper cites.
L. V. Kantorovich, “Mathematical methods of organizing and planning production,”
1939
Earlier work this paper cites.
R. Sinkhorn, “A relationship between arbitrary positive matrices and doubly stochastic matrices,”
1964
Earlier work this paper cites.
R. Sinkhorn and P. Knopp, “Concerning nonnegative matrices and doubly stochastic matrices,”
1967
Earlier work this paper cites.
J. Altschuler, J. Niles-Weed, and P. Rigollet, “Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration,” in
1974
Earlier work this paper cites.
I. Csiszár, “
1975
Earlier work this paper cites.
L. Lewin,
1981
Earlier work this paper cites.
D. Pollard, “Quantization and the method of
1982
Earlier work this paper cites.
M. J. Cullen and R. J. Purser, “An extended lagrangian theory of semi-geostrophic frontogenesis,”
1984
Earlier work this paper cites.
M. Knott and C. S. Smith, “On the optimal mapping of distributions,”
1984
Earlier work this paper cites.
F. Aurenhammer, “Power diagrams: properties, algorithms and applications,”
1987
Earlier work this paper cites.
Y. Brenier, “Décomposition polaire et réarrangement monotone des champs de vecteurs,”
1987
Earlier work this paper cites.
H. Föllmer, “Random fields and diffusion processes,” in
1988
Earlier work this paper cites.
J. A. Cuesta and C. Matrán, “Notes on the Wasserstein metric in Hilbert spaces,”
1989
Earlier work this paper cites.
L. Rüschendorf and S. T. Rachev, “A characterization of random variables with minimum l2-distance,”
1990
Earlier work this paper cites.
R. Cominetti and J. San Martín, “Asymptotic analysis of the exponential penalty trajectory in linear programming,”
1994
Earlier work this paper cites.
R. J. McCann, “A convexity principle for interacting gases,”
1997
Earlier work this paper cites.
F. Aurenhammer, F. Hoffmann, and B. Aronov, “Minkowski-type theorems and least-squares clustering,”
1998
Earlier work this paper cites.
J.-D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem,”
2000
Earlier work this paper cites.
F. Otto and C. Villani, “Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality,”
2000
Cited alongside, same era.
L. Desvillettes and C. Villani, “On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation,”
2001
Cited alongside, same era.
F. Otto, “The geometry of dissipative evolution equations: the porous medium equation,”
2001
Cited alongside, same era.
T. Mikami, “Monge’s problem with a quadratic cost by the zero-noise limit of
2004
Cited alongside, same era.
——, “On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation,”
2005
Cited alongside, same era.
K.-T. Sturm, “On the geometry of metric measure spaces,”
A. Genevay, G. Peyré, and M. Cuturi, “Learning generative models with Sinkhorn divergences,” in
2018
Later among the works it cites.
P. Rigollet and J. Weed, “Entropic optimal transport is maximum-likelihood deconvolution,”
2018
Later among the works it cites.
J. Weed, “An explicit analysis of the entropic penalty in linear programming,” in
2018
Later among the works it cites.
A. Genevay, L. Chizat, F. Bach, M. Cuturi, and G. Peyré, “Sample complexity of Sinkhorn divergences,” in
2019
Later among the works it cites.
G. Mena and J. Niles-Weed, “Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem,” in
2019
Later among the works it cites.
S. Pal, “On the difference between entropic cost and the optimal transport cost,”
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2006
Cited alongside, same era.
S. Graf and H. Luschgy,
2007
Cited alongside, same era.
C. Villani,
2008
Cited alongside, same era.
J. Lott and C. Villani, “Ricci curvature for metric-measure spaces via optimal transport,”
2009
Cited alongside, same era.
C. Léonard, “From the schrödinger problem to the monge–kantorovich problem,”
2012
Cited alongside, same era.
M. Cuturi, “Sinkhorn distances: Lightspeed computation of optimal transport,” in
2013
Cited alongside, same era.
S. Dereich, M. Scheutzow, and R. Schottstedt, “Constructive quantization: Approximation by empirical measures,” in
2013
Cited alongside, same era.
2019
Later among the works it cites.
G. Peyré and M. Cuturi, “Computational optimal transport: with applications to data science,”
2019
Later among the works it cites.
2020
Later among the works it cites.
J.-D. Benamou, W. Ijzerman, and G. Rukhaia, “An entropic optimal transport numerical approach to the reflector problem,” 2020
2020
Later among the works it cites.
L. Chizat, P. Roussillon, F. Léger, F.-X. Vialard, and G. Peyré, “Faster Wasserstein distance estimation with the Sinkhorn divergence,”
2020
Later among the works it cites.
2020
Later among the works it cites.
N. Gigli and L. Tamanini, “Benamou-Brenier and duality formulas for the entropic cost on
2020
Later among the works it cites.
M. Nutz, “Lectures on entropic optimal transport,” 2020, Lecture Notes, Columbia University
2020
Later among the works it cites.
E. Bernton, P. Ghosal, and M. Nutz, “Entropic optimal transport: geometry and large deviations,”
2021
Closest in time.
G. Conforti and L. Tamanini, “A formula for the time derivative of the entropic cost and applications,”
2021
Closest in time.
2021
Closest in time.
Q. Mérigot and B. Thibert, “Chapter 2 -optimal transport: discretization and algorithms,” in
2021
Closest in time.