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We investigate the convergence rate of the optimal entropic cost $v_\varepsilon$ to the optimal transport cost as the noise parameter $\varepsilon \downarrow 0$.
“On the Difference between Entropic Cost and the Optimal Transport Cost”, 2019
Soumik Pal · 1905
Earlier work this paper cites.
“Über Die Umkehrung Der Naturgesetze”
Schrödinger, Erwin · 1931
Earlier work this paper cites.
“Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique”
E. Schrödinger · 1932
Earlier work this paper cites.
“On the Dimension and Entropy of Probability Distributions”
A. Rényi · 1959
Earlier work this paper cites.
“Monotone (Nonlinear) Operators in Hilbert Space”
George. Minty · 1962
Earlier work this paper cites.
“A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices”
Richard Sinkhorn · 1964
Earlier work this paper cites.
“Quantitative Stability and Error Estimates for Optimal Transport Plans”
Wenbo Li and Ricardo Nochetto · 1965
Earlier work this paper cites.
“ I I -Divergence Geometry of Probability Distributions and Minimization Problems”
I. Csiszar · 1975
Earlier work this paper cites.
“Dimension, Entropy and Lyapunov Exponents”
Lai-Sang Young · 1982
Earlier work this paper cites.
“On the Scaling of Multidimensional Matrices”
Joel Franklin and Jens Lorenz · 1989
Earlier work this paper cites.
“Polar Factorization and Monotone Rearrangement of Vector-Valued Functions”
Yann Brenier · 1991
Earlier work this paper cites.
“Decomposition of Multivariate Functions”
J.. Borwein and A.. Lewis · 1992
Earlier work this paper cites.
“Boundary Regularity of Maps with Convex Potentials”
Luis. Caffarelli · 1992
Earlier work this paper cites.
“Entropy Minimization, DAD Problems, and Doubly Stochastic Kernels”
J.. Borwein, A.. Lewis and R.. Nussbaum · 1994
Earlier work this paper cites.
“Asymptotic Analysis of the Exponential Penalty Trajectory in Linear Programming”
R. Cominetti and J. Martín · 1994
Earlier work this paper cites.
“Existence and Uniqueness of Monotone Measure-Preserving Maps”
Robert. McCann · 1995
Earlier work this paper cites.
“Boundary Regularity of Maps with Convex Potentials–II”
Luis. Caffarelli · 1996
Earlier work this paper cites.
“Techniques in Fractal Geometry”
Kenneth Falconer · 1997
Earlier work this paper cites.
“Entropy Minimization and Schrödinger Processes in Infinite Dimensions”
Hans Föllmer and Nina Gantert · 1997
Earlier work this paper cites.
“Closedness of Sum Spaces and the Generalized Schrödinger Problem”
L. Rüschendorf and W. Thomsen · 1998
Earlier work this paper cites.
“A geometrical approach to monotone functions in ℝ n \mathbb{R}^{n} ”
Giovanni Alberti and Luigi Ambrosio · 1999
Earlier work this paper cites.
“Functions of Bounded Variation and Free Discontinuity Problems”, Oxford Mathematical Monographs
Luigi Ambrosio, Nicola Fusco and Diego Pallara · 2000
Earlier work this paper cites.
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C. Léonard · 2001
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