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This paper continues the investigation of `Wasserstein-like' transportation distances for probability measures on discrete sets.
Logarithmic Sobolev inequalities for finite Markov chains
P. Diaconis and L. Saloff-Coste · 1996
Earlier work this paper cites.
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
J.-D. Benamou and Y. Brenier · 2000
Earlier work this paper cites.
The geometry of dissipative evolution equations: the porous medium equation
F. Otto · 2001
Earlier work this paper cites.
Identification of asymptotic decay to self-similarity for one-dimensional filtration equations
L. Gosse and G. Toscani · 2006
Earlier work this paper cites.
Gradient flows in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
Earlier work this paper cites.
Mass transportation and rough curvature bounds for discrete spaces
A.-I. Bonciocat and K.-Th. Sturm · 2009
Cited alongside, same era.
Optimal transport, Old and new
C. Villani · 2009
Cited alongside, same era.
The heat equation on manifolds as a gradient flow in the Wasserstein space
M. Erbar · 2010
Cited alongside, same era.
On the heat flow on metric measure spaces: existence, uniqueness and stability
N. Gigli · 2010
Cited alongside, same era.
Gradient flows of the entropy for finite Markov chains
J. Maas · 2011
Cited alongside, same era.
Geodesic convexity of the relative entropy in reversible Markov chains
A. Mielke
Cited in the paper.
Transport equation with nonlocal velocity in Wasserstein spaces: Convergence of numerical schemes
B. Piccoli and F. Rossi
Cited in the paper.
A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems
A. Mielke · 2011
Later among the works it cites.
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
S. Serfaty · 2011
Later among the works it cites.
Fokker-Planck equations for a free energy functional or Markov process on a graph
S.-N. Chow, W. Huang, Y. Li, and H. Zhou · 2012
Closest in time.
Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow
M. Colombo and M. Gobbino · 2012
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Ricci curvature of finite Markov chains via convexity of the entropy
M. Erbar and J. Maas · 2012
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