Kantorovich distance on finite metric spaces: Arens–Eells norm and CUT norms
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Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall Inc, Englewood Cliffs (1993)
Aliaga, R.J., Rueda Zoca, A.: Points of differentiability of the norm in Lipschitz-free spaces. J. Math. Anal. Appl. 489(2), 124171 (2020). https://doi.org/10.1016/j.jmaa.2020.124171
Amari, S., Nagaoka, H.: Methods of Information Geometry. American Mathematical Society, translated from the 1993 Japanese original by Daishi Harada (2000)
Amari, S., Karakida, R., Oizumi, M.: Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem. Inf. Geom. 1(1), 13–37 (2018). https://doi.org/10.1007/s41884-018-0002-8
Arens, R.F., Eells, J. Jr.: On embedding uniform and topological spaces. Pac. J. Math. 6, 397–403 (1956). http://projecteuclid.org/euclid.pjm/1103043959
Bandelt, H.J., Dress, A.W.M.: A canonical decomposition theory for metrics on a finite set. Adv. Math. 92(1), 47–105 (1992). https://doi.org/10.1016/0001-8708(92)90061-O
Barvinok, A.: A Course in Convexity, Graduate Studies in Mathematics, vol. 54. American Mathematical Society, Providence (2002)
Bassetti, F., Gualandi, S., Veneroni, M.: On the computation of Kantorovich–Wasserstein distances between two-dimensional histograms by uncapacitated minimum cost flows. SIAM J. Optim. 30(3), 2441–2469 (2020). https://doi.org/10.1137/19M1261195
Bergman, G.M.: Mapping radii of metric spaces. Pac. J. Math. 236(2), 223–261 (2008). https://doi.org/10.2140/pjm.2008.236.223
Buneman, P.: A note on the metric properties of trees. J. Combin. Theory Ser. B 17, 48–50 (1974). https://doi.org/10.1016/0095-8956(74)90047-1
Cabrelli, C.A., Molter, U.M.: The Kantorovich metric for probability measures on the circle. J. Comput. Appl. Math. 57(3), 345–361 (1995). https://doi.org/10.1016/0377-0427(93)E0213-6
Deza, M.M., Laurent, M.: Geometry of Cuts and Metrics, Algorithms and Combinatorics, vol. 15. Springer, Berlin (1997). https://doi.org/10.1007/978-3-642-04295-9
Farmer, J.D.: Extreme points of the unit ball of the space of Lipschitz functions. Proc. Am. Math. Soc. 121(3), 807–813 (1994). https://doi.org/10.2307/2160280
Gini, C.: Di una misura della dissomiglianza di due gruppi di quantità e delle sue applicazioni allo studio delle relazioni statistiche. Atti R Ist Veneto Sc Lett Arti LXXIV, 185–213 (1914)
Godard, A.: Tree metrics and their Lipschitz-free spaces. Proc. Am. Math. Soc. 138(12), 4311–4320 (2010). https://doi.org/10.1090/S0002-9939-2010-10421-5
Kloeckner, B.R.: A geometric study of Wasserstein spaces: ultrametrics. Mathematika 61(1), 162–178 (2015). https://doi.org/10.1112/S0025579314000059
Kruskal Jr., J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956). https://doi.org/10.2307/2033241
Megginson, R.E.: An Introduction to Banach Space Theory, Graduate Texts in Mathematics, vol. 183. Springer, New York (1998). https://doi.org/10.1007/978-1-4612-0603-3
Mendivil, F.: Computing the Monge–Kantorovich distance. Comput. Appl. Math. 36(3), 1389–1402 (2017). https://doi.org/10.1007/s40314-015-0303-7
Peyré, G., Cuturi, M.: Computational optimal transport. Found. Trends Mach. Learn. 11(5–6), 355–607. arXiv:1803.00567v2 (2019)
Pistone, G., Rapallo, F., Rogantin, M.P.: Finite space Kantorovich problem with an MCMC of table moves. Electron. J. Stat. 15(1), 880–907 (2021). https://doi.org/10.1214/21-EJS1804
Santambrogio, F.: Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling. Birkhäuser (2015)
Smarzewski, R.: Extreme points of unit balls in Lipschitz function spaces. Proc. Am. Math. Soc. 125(5), 1391–1397 (1997). https://doi.org/10.1090/S0002-9939-97-03866-5
Sommerfeld, M., Munk, A.: Inference for empirical Wasserstein distances on finite spaces. J. R. Stat. Soc. Ser. B Stat. Methodol. 80(1), 219–238 (2018). https://doi.org/10.1111/rssb.12236
Villani, C.: Optimal Transport: Old and New. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (2008). https://books.google.it/books?id=hV8o5R7_5tkC
Weaver, N.: Lipschitz Algebras, 2nd edn. World Scientific Publishing Co. Pte. Ltd., Hackensack (2018)