Homogenisation of one-dimensional discrete optimal transport

Al Reda, 2017, Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance, vol. 17, 400 Ambrosio, 2008, Gradient Flows in Metric Spaces and in the Space of Probability Measures Benamou, 2000, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numer. Math., 84, 375, 10.1007/s002110050002 Burago, 2001, A Course in Metric Geometry, vol. 33 Chow, 2012, Fokker-Planck equations for a free energy functional or Markov process on a graph, Arch. Ration. Mech. Anal., 203, 969, 10.1007/s00205-011-0471-6 Disser, 2015, On gradient structures for Markov chains and the passage to Wasserstein gradient flows, Netw. Heterog. Media, 10, 233, 10.3934/nhm.2015.10.233 Dondl Erbar, 2018, Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature, J. Funct. Anal., 274, 3056, 10.1016/j.jfa.2018.03.011 Erbar, 2017, Ricci curvature bounds for weakly interacting Markov chains, Electron. J. Probab., 22, 10.1214/17-EJP49 Erbar, 2012, Ricci curvature of finite Markov chains via convexity of the entropy, Arch. Ration. Mech. Anal., 206, 997, 10.1007/s00205-012-0554-z Erbar, 2014, Gradient flow structures for discrete porous medium equations, Discrete Contin. Dyn. Syst., 34, 1355, 10.3934/dcds.2014.34.1355 Erbar, 2015, Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models, Ann. Fac. Sci. Toulouse, 24, 781, 10.5802/afst.1464 Eymard, 2000, Finite volume methods, vol. VII, 713, 10.1016/S1570-8659(00)07005-8 Fathi, 2016, Entropic Ricci curvature bounds for discrete interacting systems, Ann. Appl. Probab., 26, 1774, 10.1214/15-AAP1133 García Trillos Gigli, 2013, Gromov–Hausdorff convergence of discrete transportation metrics, SIAM J. Math. Anal., 45, 879, 10.1137/120886315 Gladbach Jordan, 1998, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal., 29, 1, 10.1137/S0036141096303359 Maas, 2011, Gradient flows of the entropy for finite Markov chains, J. Funct. Anal., 261, 2250, 10.1016/j.jfa.2011.06.009 Mielke, 2011, A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, Nonlinearity, 24, 1329, 10.1088/0951-7715/24/4/016 Mielke, 2013, Geodesic convexity of the relative entropy in reversible Markov chains, Calc. Var. Partial Differ. Equ., 48, 1, 10.1007/s00526-012-0538-8 Mielke, 2016, On evolutionary Γ-convergence for gradient systems, vol. 3, 187 Mielke, 2016, Deriving effective models for multiscale systems via evolutionary Γ-convergence, 235 Peyré, 2019, Computational optimal transport, Found. Trends Mach. Learn., 11, 355, 10.1561/2200000073 Santambrogio, 2015, Optimal Transport for Applied Mathematicians, vol. 87 Villani, 2003, Topics in Optimal Transportation, vol. 58 Villani, 2008