Gradient flows of the entropy for finite Markov chains

Ambrosio, 2008, Gradient Flows in Metric Spaces and in the Space of Probability Measures

Ambrosio, 2009, Existence and stability for Fokker–Planck equations with log-concave reference measure, Probab. Theory Related Fields, 145, 517, 10.1007/s00440-008-0177-3

Benamou, 2000, A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem, Numer. Math., 84, 375, 10.1007/s002110050002

Bhatia, 2007, Positive Definite Matrices

Bonciocat, 2009, Mass transportation and rough curvature bounds for discrete spaces, J. Funct. Anal., 256, 2944, 10.1016/j.jfa.2009.01.029

Carrillo, 2010, Nonlinear mobility continuity equations and generalized displacement convexity, J. Funct. Anal., 258, 1273, 10.1016/j.jfa.2009.10.016

S.-N. Chow, W. Huang, Y. Li, H. Zhou, Fokker–Planck equations for a free energy functional or Markov process on a graph, preprint.

Dahl, 2000, A note on diagonally dominant matrices, Linear Algebra Appl., 317, 217, 10.1016/S0024-3795(00)00178-6

Dolbeault, 2009, A new class of transport distances between measures, Calc. Var. Partial Differential Equations, 34, 193, 10.1007/s00526-008-0182-5

Erbar, 2010, The heat equation on manifolds as a gradient flow in the Wasserstein space, Ann. Inst. Henri Poincaré Probab. Stat., 46, 1, 10.1214/08-AIHP306

Fang, 2010, Wasserstein space over the Wiener space, Probab. Theory Related Fields, 146, 535, 10.1007/s00440-009-0199-5

Gigli, 2010, On the heat flow on metric measure spaces: existence, uniqueness and stability, Calc. Var. Partial Differential Equations, 39, 101, 10.1007/s00526-009-0303-9

Gigli

Jordan, 1998, The variational formulation of the Fokker–Planck equation, SIAM J. Math. Anal., 29, 1, 10.1137/S0036141096303359

Jost, 2008, Riemannian Geometry and Geometric Analysis

Lin, 2010, Ricci curvature and eigenvalue estimate on locally finite graphs, Math. Res. Lett., 17, 343, 10.4310/MRL.2010.v17.n2.a13

Lott, 2009, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2), 169, 903, 10.4007/annals.2009.169.903

McAdams, 1954

Ohta, 2009, Heat flow on Finsler manifolds, Comm. Pure Appl. Math., 62, 1386, 10.1002/cpa.20273

Ollivier, 2007, Ricci curvature of metric spaces, C. R. Math. Acad. Sci. Paris, 345, 643, 10.1016/j.crma.2007.10.041

Ollivier, 2009, Ricci curvature of Markov chains on metric spaces, J. Funct. Anal., 256, 810, 10.1016/j.jfa.2008.11.001

Ollivier

Otto, 2001, The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Differential Equations, 26, 101, 10.1081/PDE-100002243

Otto, 2000, Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality, J. Funct. Anal., 173, 361, 10.1006/jfan.1999.3557

Savaré, 2007, Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds, C. R. Math. Acad. Sci. Paris, 345, 151, 10.1016/j.crma.2007.06.018

Sturm, 2006, On the geometry of metric measure spaces. I and II, Acta Math., 196, 65, 10.1007/s11511-006-0002-8

Villani, 2003, Topics in Optimal Transportation, vol. 58

Villani, 2009, Optimal Transport, Old and New, vol. 338