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We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric.
On Harmonic and Killing Vector Fields
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The real Monge-Ampére equation and affine flat structures
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Conservative Diffusions
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The Density Manifold and Configuration Space Quantization
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The Convenient Setting of Global Analysis
A. Kriegl and P. W. Michor · 1997
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The Variational Formulation of the Fokker–Planck Equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
F. Otto and C. Villani · 2000
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Polar Factorization of Maps on Riemannian Manifolds
R. J. McCann · 2001
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The Geometry of Dissipative Evolution Equations: The Porous Medium Equation
F. Otto · 2001
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Constrained Steepest Descent in the 2-Wasserstein Metric
E. A. Carlen and W. Gangbo · 2003
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Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media
J. A. Carrillo, R. J. McCann, and C. Villani · 2006
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On the Geometry of Metric Measure Spaces
K.-T. Sturm · 2006
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Information geometry of divergence functions
S. Amari and A. Cichocki · 2010
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Gradient Flows of the Entropy for Finite Markov Chains
J. Maas · 2011
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A Gradient Structure for Reaction–diffusion Systems and for Energy-Drift-Diffusion Systems
A. Mielke · 2011
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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
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Information Geometry and Its Applications
S. Amari · 2016
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A Study of Stochastic Differential Equations and Fokker-Planck Equations with Applications
W. Li · 2016
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Some Geometric Calculations on Wasserstein Space
J. Lott · 2008
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Ricci Curvature for Metric-Measure Spaces via Optimal Transport
J. Lott and C. Villani · 2009
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Optimal Transport: Old and New
C. Villani · 2009
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Entropic measure and Wasserstein diffusion
M.-K. von Renesse and K.-T. Sturm · 2009
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Second Order Analysis on (P2(M),W2)
N. Gigli
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Information geometry
N. Ay, J. Jost, H. V. Lê, and L. Schwachhöfer · 2017
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A Discrete Schrodinger Equation via Optimal Transport on Graphs
S.-N. Chow, W. Li, and H. Zhou · 2017
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Entropy Dissipation of Fokker-Planck Equations on Graphs
S.-N. Chow, W. Li, and H. Zhou · 2017
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Geodesic of minimal length in the set of probability measures on graphs
W. Gangbo, W. Li, and C. Mou · 2017
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