The dynamical Schrödinger problem in abstract metric spaces

DOI10.1016/j.aim.2023.109100zbMath1516.49013arXiv2012.12005OpenAlexW3114114809MaRDI QIDQ6103491

Léonard Monsaingeon, Dmitry A. Vorotnikov, Luca Tamanini

Publication date: 5 June 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.12005

zbMATH Keywords

gradient flowFisher informationGamma-convergencemetric geometryoptimal transportSchrödinger problem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20)

Related Items (3)

Hidden Dissipation and Convexity for Kimura Equations ⋮ Monge-Ampère gravitation as a \(\Gamma \)-limit of good rate functions ⋮ Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps

Cites Work

• Unnamed Item
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• On the relation between optimal transport and Schrödinger bridges: a stochastic control viewpoint
• A survey of the Schrödinger problem and some of its connections with optimal transport
• From the Schrödinger problem to the Monge-Kantorovich problem
• Nonlinear mobility continuity equations and generalized displacement convexity
• From large deviations to Wasserstein gradient flows in multiple dimensions
• Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
• A new class of transport distances between measures
• The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
• A convexity principle for interacting gases
• Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm
• Monge's problem with a quadratic cost by the zero-noise limit of \(h\)-path processes
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Dynamical aspects of the generalized Schrödinger problem via Otto calculus -- a heuristic point of view
• A formula for the time derivative of the entropic cost and applications
• Second order differentiation formula on \(\mathsf{RCD}^*(K,N)\) spaces
• Quadratically regularized optimal transport
• Orlicz space regularization of continuous optimal transport problems
• Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below
• An optimal transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm
• The Schrödinger problem on the non-commutative Fisher-Rao space
• The globalization theorem for the curvature-dimension condition
• Gradient flows and evolution variational inequalities in metric spaces. I: structural properties
• An entropic interpolation proof of the HWI inequality
• Benamou-Brenier and duality formulas for the entropic cost on \(\mathsf{RCD}^*(K,N)\) spaces
• Around the entropic talagrand inequality
• Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
• A geometric perspective on regularized optimal transport
• The continuity equation on metric measure spaces
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction
• On the differential structure of metric measure spaces and applications
• Quadratically Regularized Optimal Transport on Graphs
• Fixed Point Theory in Distance Spaces
• Optimal Transportation Problem by Stochastic Optimal Control
• Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
• Variational processes and stochastic versions of mechanics
• Remarks on Some Fixed Point Theorems
• The Variational Formulation of the Fokker--Planck Equation
• Weak topologies in complete $CAT(0)$ metric spaces
• An entropy minimization approach to second-order variational mean-field games
• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
• Iterative Bregman Projections for Regularized Transportation Problems
• A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost
• Eulerian Calculus for the Contraction in the Wasserstein Distance
• Convergence of Entropic Schemes for Optimal Transport and Gradient Flows
• The Research Program of Stochastic Deformation (with a View Toward Geometric Mechanics)
• Optimal Transport

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