Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 27
Number of page(s) 17
DOI https://doi.org/10.1051/cocv/2026012
Published online 10 April 2026
  1. C. Villani, Topics in optimal transportation, vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [Google Scholar]
  2. C. Villani, Optimal transport, vol. 338 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (2009). [Google Scholar]
  3. F. Santambrogio, Optimal transport for applied mathematicians, vol. 87 of Progress in Nonlinear Differential Equations and their Applications. Birkhauser/Springer, Cham (2015). [Google Scholar]
  4. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appi. Math. 44 (1991) 375–417. [Google Scholar]
  5. R.J. McCann, Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80 (1995) 309–323. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Leonard, A survey of the Schrödinger problem and some of its connections with optimal transport. Discrete Contin. Dyn. Syst. 34 (2014) 1533–1574. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Nutz, Introduction to entropic optimal transport in Lecture notes, Columbia University (2021). [Google Scholar]
  8. A. Figalli, On the Monge-Ampere equation. Astérisque 1148 (2019) 477–503. [Google Scholar]
  9. M. Cuturi, Sinkhorn distances: lightspeed computation of optimal transport, Advances in Neural Information Processing Systems, vol. 26, edited by C. Burges, L. Bottou, M. Welling, Z. Ghahramani and K. Weinberger. Curran Associates, Inc. (2013). [Google Scholar]
  10. J. Altschuler, J. Niles-Weed and P. Rigollet, Near-linear time approximation algorithms for optimal transport via sinkhorn iteration. Adv. Neural Inform. Process. Syst. 30 (2017) 1961–1971. [Google Scholar]
  11. G. Peyre and M. Cuturi, Computational optimal transport. Found. Trends Mach. Learn. 11 (2019) 355–607. [Google Scholar]
  12. C. Leonard, From the Schrödinger problem to the Monge-Kantorovich problem. J. Funct. Anal. 262 (2012) 1879–1920. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Carlier, V. Duval, G. Peyre and B. Schmitzer, Convergence of entropic schemes for optimal transport and gradient flows. SIAM J. Math. Anal. 49 (2017) 1385–1418. [CrossRef] [MathSciNet] [Google Scholar]
  14. N. Gigli and L. Tamanini, Second order differentiation formula on RCD+ (K, N) spaces. J. Eur. Math. Soc. 23 (2021) 1727–1795. [Google Scholar]
  15. M. Nutz and J. Wiesel, Entropic optimal transport: convergence of potentials. Probab. Theory Related Fields 184 (2022) 401–424. [Google Scholar]
  16. A. Chiarini, G. Conforti, G. Greco and L. Tamanini, Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability. Commun. Part. Differ. Equ. 48 (2023) 895–943. [Google Scholar]
  17. S. Adams, N. Dirr, M.A. Peletier and J. Zimmer, From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage. Commun. Math. Phys. 307 (2011) 791–815. [Google Scholar]
  18. M.H. Duong, V. Laschos and M. Renger, Wasserstein gradient flows from large deviations of many-particle limits. ESAIM Control Optim. Calc. Var. 19 (2013) 1166–1188. [Google Scholar]
  19. M. Erbar, J. Maas and D.R.M. Renger, From large deviations to Wasserstein gradient flows in multiple dimensions. Electron. Commun. Probab. 20 (2015) 12. [Google Scholar]
  20. S. Pal, On the difference between entropic cost and the optimal transport cost. Ann. Appi. Probab. 34 (2024) 1003–1028. [Google Scholar]
  21. L. Chizat, P. Roussillon, F. Leger, F.-X. Vialard and G. Peyre, Faster Wasserstein distance estimation with the Sinkhorn divergence. Adv. Neural Inform. Process. Syst. 33 (2020) 2257–2269. [Google Scholar]
  22. G. Conforti and L. Tamanini, A formula for the time derivative of the entropic cost and applications. J. Funct. Anal. 280 (2021) Paper No. 108964. [Google Scholar]
  23. G. Carlier, P. Pegon and L. Tamanini, Convergence rate of general entropic optimal transport costs. Calc. Var. Part. Differ. Equ. 62 (2023) Paper No. 116. [Google Scholar]
  24. S. Eckstein and M. Nutz, Convergence rates for regularized optimal transport via quantization. Math. Oper. Res. 49 (2024) 1223–1240. [Google Scholar]
  25. H. Malamut and M. Sylvestre, Convergence rates of the regularized optimal transport: disentangling suboptimality and entropy. SIAM J. Math. Anal. 57 (2025) 2533–2558. [Google Scholar]
  26. A.-A. Pooladian and J. Niles-Weed, Entropic estimation of optimal transport maps. arXiv preprint arXiv:2109.12004 (2021). [Google Scholar]
  27. R.T. Rockafellar, Convex analysis, vol. No. 28 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ (1970). [Google Scholar]
  28. R. Cominetti and J. San Martin, Asymptotic analysis of the exponential penalty trajectory in linear programming. Math. Program. 67 (1994) 169–187. [Google Scholar]
  29. A. Delalande, Nearly tight convergence bounds for semi-discrete entropic optimal Transport, in International Conference on Artificial Intelligence and Statistics. PMLR (2022) 1619–1642. [Google Scholar]
  30. R. Sadhu, Z. Goldfeld and K. Kato, Approximation rates of entropic maps in semidiscrete optimal transport. Electron. Commun. Probab. 30 (2025) Paper No. 36. [Google Scholar]
  31. A. Gonzalez-Sanz and M. Nutz, Sparsity of quadratically regularized optimal transport: Scalar case. arXiv preprint arXiv:2410.03353 (2024). [Google Scholar]
  32. L.A. Caffarelli, Monotonicity properties of optimal transportation and the FKG and related inequalities. Commun. Math. Phys. 214 (2000) 547–563. [Google Scholar]
  33. S. Chewi and A.-A. Pooladian, An entropic generalization of Caffarelli's contraction theorem via covariance inequalities. C. R. Math. Acad. Sci. Paris 361 (2023) 1471–1482. [Google Scholar]
  34. M. Fathi, N. Gozlan and M. Prod'homme, A proof of the Caffarelli contraction theorem via entropic regularization. Calc. Var. Part. Differ. Equ. 59 (2020) Paper No. 96. [Google Scholar]
  35. D. Bakry, I. Gentil and M. Ledoux, Analysis and geometry of Markov diffusion operators, vol. 348 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Cham (2014). [Google Scholar]
  36. N. Gigli, On Holder continuity-in-time of the optimal transport map towards measures along a curve. Proc. Edinb. Math. Soc. 54 (2011) 401–409. [Google Scholar]
  37. F. Soudsky, A. Molchanova and T. Roskovec, Interpolation between Holder and Lebesgue spaces with applications. J. Math. Anal. Appl. 466 (2018) 160–168. [Google Scholar]
  38. L.C. Evans, Partial differential equations, vol. 19 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, RI (2010). [Google Scholar]
  39. M. Gelbrich, On a formula for the L2 Wasserstein metric between measures on Euclidean and Hilbert spaces. Math. Nachr. 147 (1990) 185–203. [Google Scholar]
  40. H. Janati, B. Muzellec, G. Peyre and M. Cuturi. Entropic optimal transport between unbalanced gaussian measures has a closed form. Adv. Neural Inform. Process. Syst. 33 (2020) 10468–10479. [Google Scholar]
  41. E. del Barrio and J.-M. Loubes, The statistical effect of entropic regularization in optimal transportation. arXiv preprint arXiv:2006.05199 (2020). [Google Scholar]
  42. A. Mallasto, A. Gerolin and H.Q. Minh, Entropy-regularized 2-Wasserstein distance between Gaussian measures. Inf. Geom. 5 (2022) 289–323. [Google Scholar]
  43. P. Del Moral and A. Niclas, A Taylor expansion of the square root matrix function. J. Math. Anal. Appl. 465 (2018) 259–266. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.