Fetching the paper…
Reading the bibliography…
We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the space of probability measures supported on the nodes with respect to the discrete Wasserstein metric.
Some remarks on tensor fields and curvature
Kentaro Yano · 1952
Earlier work this paper cites.
Some integral formulas and their applications
Kentaro Yano · 1958
Earlier work this paper cites.
The variational formulation of the Fokker-Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
Earlier work this paper cites.
On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis
Peter A Markowich and Cédric Villani · 2000
Earlier work this paper cites.
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
Felix Otto and Cédric Villani · 2000
Earlier work this paper cites.
Entropic methods for the study of the long time behavior of kinetic equations
Laurent Desvillettes and Cédric Villani · 2001
Earlier work this paper cites.
The geometry of dissipative evolution equations: the porous medium equation
Felix Otto · 2001
Earlier work this paper cites.
Constrained steepest descent in the 2-Wasserstein metric
Eric Carlen and Wilfrid Gangbo · 2003
Earlier work this paper cites.
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
José A Carrillo, Robert J McCann and Cédric Villani · 2003
Earlier work this paper cites.
Topics in Optimal transportation
Cédric Villani · 2003
Cited alongside, same era.
Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2006
Cited alongside, same era.
Optimal transport: old and new
Cédric Villani · 2008
Cited alongside, same era.
Gradient flows of the entropy for finite Markov chains
Jan Maas · 2011
Cited alongside, same era.
A gradient structure for reactionÐdiffusion systems and for energy-drift-diffusion systems
Alexander Mielke · 2011
Cited alongside, same era.
Fokker-Planck equations for a free energy functional or Markov process on a graph
Shui-Nee Chow, Wen Huang, Yao Li and Haomin Zhou · 2012
Cited alongside, same era.
Geodesic convexity of the relative entropy in reversible Markov chains
Alexander Mielke · 2013
Later among the works it cites.
On the equivalence of the entropic curvature-dimension condition and BochnerÕs inequality on metric measure spaces
Matthias Erbar, Kazumasa Kuwada, and Karl-Theodor Sturm · 2015
Later among the works it cites.
Long-time behavior of a finite volume discretization for a fourth order diffusion equation,
Jan Maas and Daniel Matthes · 2015
Later among the works it cites.
Entropy dissipation semi-discretization schemes for Fokker-Planck equations
Shui-Nee Chow, Luca Dieci, Wuchen Li and Haomin Zhou · 2016
Later among the works it cites.
Gradient flow structure for McKean-Vlasov equations on discrete spaces
M. Erbar, M. Fathi, V. Laschos and A. Schlichting · 2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Ricci curvature of finite Markov chains via convexity of the entropy
Matthias Erbar and Jan Maas · 2012
Cited alongside, same era.
Gradient flow structures for discrete porous medium equations
Matthias Erbar and Jan Maas · 2012
Cited alongside, same era.
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
Jean-David Benamou and Yann Brenier
Cited in the paper.
Convergence to global equilibrium for FokkerÐPlanck equations on a graph and Talagrand-type inequalities
R. Che, W. Huang, Y. Li and P. Tetali
Cited in the paper.
Entropic Ricci curvature bounds for discrete interacting systems,
Max Fathi and Jan Maas · 2016
Later among the works it cites.
A study of stochastic differential equations and Fokker-Planck equations with applications
Wuchen Li · 2016
Later among the works it cites.
Continuous-Flow Graph Transportation Distances
Justin Solomon, Raif Rustamov, Leonidas Guibas, Adrian Butscher · 2016
Later among the works it cites.