Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 42
Number of page(s) 17
DOI https://doi.org/10.1051/cocv/2024031
Published online 08 May 2024
  1. D. Bilyk, Roth’s orthogonal function method in discrepancy theory and some new Connections, in A Panorama of Discrepancy Theory, Vol. 2107 of Lecture Notes in Mathematics. Springer, Cham (2014) 71–158. [CrossRef] [Google Scholar]
  2. M. Blümlinger, Asymptotic distribution and weak convergence on compact Riemannian manifolds. Monatsh. Math. 110 (1990) 177–188. [CrossRef] [MathSciNet] [Google Scholar]
  3. F.E. Su, A LeVeque-type lower bound for discrepancy, in Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA). Springer, Berlin (2000) 448–458. [CrossRef] [Google Scholar]
  4. F.E. Su, Discrepancy convergence for the drunkard’s walk on the sphere. Electron. J. Probab. 6 (2021) 20. [Google Scholar]
  5. F.E. Su, Convergence of random walks on the circle generated by an irrational rotation. Trans. Am. Math. Soc. 350 (1998) 3717–3741. [CrossRef] [Google Scholar]
  6. A. Nourmohammadi, H. Eskandari, M. Fathi and M. Aghdasi, A mathematical model for supermarket location problem with stochastic station demands. Procedia CIRP 72 (2018) 444–449. [CrossRef] [Google Scholar]
  7. M. Talagrand, Matching theorems and empirical discrepancy computations using majorizing measures. J. Am. Math. Soc. 7 (1994) 455–537. [CrossRef] [Google Scholar]
  8. L. Ambrosio, F. Stra and D. Trevisan, A PDE approach to a 2-dimensional matching problem. Probab. Theory Related Fields 173 (2019) 433–477. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Bolley, A. Guillin and C. Villani, Quantitative concentration inequalities for empirical measures on non-compact spaces. Probab. Theory Related Fields 137 (2007) 541–593. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Santambrogio, Optimal Transport for Applied Mathematicians, Vol. 87 of Progress in Nonlinear Differential Equations and their Applications. Birkhüauser/Springer, Cham (2015). [CrossRef] [Google Scholar]
  11. C. Villani, Topics in Optimal Transportation, Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [CrossRef] [Google Scholar]
  12. L. Brown and S. Steinerberger, On the Wasserstein distance between classical sequences and the Lebesgue measure. Trans. Am. Math. Soc. 373 (2020) 8943–8962. [CrossRef] [Google Scholar]
  13. L. Brown and S. Steinerberger, Positive-definite functions, exponential sums and the greedy algorithm: a curious phenomenon. J. Complexity 61 (2020) 101485. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Steinerberger, A Wasserstein inequality and minimal Green energy on compact manifolds. J. Funct. Anal. 281 (2021) 109076. [CrossRef] [Google Scholar]
  15. D.G. Aronson, Addendum: “Non-negative solutions of linear parabolic equations” (Ann. Scuola Norm. Sup. Pisa (3) 22 (1968) 607–694). Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1971) 221–228. [MathSciNet] [Google Scholar]
  16. P. Li and S.-T. Yau, On the parabolic kernel of the Schröodinger operator. Acta Math. 156 (1986) 153–201. [CrossRef] [MathSciNet] [Google Scholar]
  17. B. Piccoli, F. Rossi and M. Tournus, A Wasserstein norm for signed measures, with application to non-local transport equation with source term. Commun. Math. Sci. 21 (2023) 1279–1301. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Bubenik and A. Elchesen, Universality of persistence diagrams and the bottleneck and Wasserstein distances. Comput. Geom. 105 (2022) 101882. [CrossRef] [Google Scholar]
  19. E. Mainini, A description of transport cost for signed measures. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 390(Teoriya Pred., Dinamicheskie Sistemy, Kombinatornye Metody. XX) 147–181 (2011) 308–309. [Google Scholar]
  20. M. Liero, A. Mielke and G. Savaré, Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures. Invent. Math. 211 (2018) 969–1117. [CrossRef] [MathSciNet] [Google Scholar]
  21. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard, Unbalanced optimal transport: dynamic and Kantorovich formulations. J. Funct. Anal. 274 (2018) 3090–3123. [Google Scholar]
  22. L. Chizat, Unbalanced Optimal Transport: Models, Numerical Methods, Applications. Theses, Université Paris sciences et lettres (2017). [Google Scholar]
  23. A. Figalli, The optimal partial transport problem. Arch. Ration. Mech. Anal. 195 (2010) 533–560. [Google Scholar]
  24. A. Figalli and N. Gigli, A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. J. Math. Pures Appl. 94 (2010) 107–130. [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.