Some geometric calculations on Wasserstein space

From MaRDI portal
Publication:934581

DOI10.1007/s00220-007-0367-3zbMath1144.58007arXivmath/0612562OpenAlexW2027258435MaRDI QIDQ934581

John Lott

Publication date: 30 July 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612562




Related Items

Geometry of matrix decompositions seen through optimal transport and information geometryThe Dirichlet-Ferguson diffusion on the space of probability measures over a closed Riemannian manifoldA GENERALIZATION OF HAUSDORFF DIMENSION APPLIED TO HILBERT CUBES AND WASSERSTEIN SPACESOptimal transport and Perelman's reduced volumeRicci curvature, isoperimetry and a non-additive entropyA Unification of Weighted and Unweighted Particle FiltersGeometry on the Wasserstein space over a compact Riemannian manifoldWhen optimal transport meets information geometryTransport information geometry: Riemannian calculus on probability simplexTime discretizations of Wasserstein–Hamiltonian flowsMeasure-Valued Spline Curves: An Optimal Transport ViewpointNeural Parametric Fokker--Planck EquationOn the Lagrangian structure of quantum fluid modelsOptimal transport and large number of particlesOn the relation between geometrical quantum mechanics and information geometryGlobally optimal joint image segmentation and shape matching based on Wasserstein modesAn intrinsic parallel transport in Wasserstein spaceThe Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure SpacesThe Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flowAffine statistical bundle modeled on a Gaussian Orlicz-Sobolev spaceWasserstein information matrixA lack of Ricci bounds for the entropic measure on Wasserstein space over the interval\(W\)-entropy and Langevin deformation on Wasserstein space over Riemannian manifoldsWasserstein Riemannian geometry of Gaussian densitiesNatural gradient via optimal transportHopf-Cole transformation via generalized Schrödinger bridge problemMaster equation for finite state mean field games with additive common noiseWasserstein geometry of Gaussian measuresDifferential forms on Wasserstein space and infinite-dimensional Hamiltonian systemsOn the pseudo-manifold of quantum statesOn differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equationsPoisson geometry and first integrals of geostrophic equationsInformation Geometry of Smooth Densities on the Gaussian Space: Poincaré InequalitiesA GEOMETRIC STUDY OF WASSERSTEIN SPACES: HADAMARD SPACESInformation geometry and non-equilibrium thermodynamic relations in the over-damped stochastic processesThe Camassa-Holm equation as an incompressible Euler equation: a geometric point of viewEffective diffusion in thin structures via generalized gradient systems and EDP-convergenceOptimal transport natural gradient for statistical manifolds with continuous sample spaceOptimal transport and dynamics of expanding circle maps acting on measuresEntropic measure and Wasserstein diffusionSubmanifolds, isoperimetric inequalities and optimal transportationA partial Laplacian as an infinitesimal generator on the Wasserstein spaceFokker-Planck equations for a free energy functional or Markov process on a graphUnnamed Item\(W\)-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifoldsPROJECTIONS ONTO THE CONE OF OPTIMAL TRANSPORT MAPS AND COMPRESSIBLE FLUID FLOWSA Rademacher-type theorem on \(L^2\)-Wasserstein spaces over closed Riemannian manifoldsPropagation of chaos for mean field rough differential equationsDifferential Geometric Heuristics for Riemannian Optimal Mass TransportationStochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger BridgeScaling and entropy for the RG-2 flowSecond-order models for optimal transport and cubic splines on the Wasserstein SpaceGeometric hydrodynamics and infinite-dimensional Newton’s equationsA geometric perspective on regularized optimal transportWasserstein Hamiltonian flowsAn invariance principle for gradient flows in the space of probability measuresA Lecture About the Use of Orlicz Spaces in Information GeometrySecond order analysis on (𝒫₂(ℳ),𝒲₂)



Cites Work