A PDE approach to a 2-dimensional matching problem

DOI10.1007/s00440-018-0837-xzbMath1480.60017arXiv1611.04960OpenAlexW2963434094WikidataQ62043464 ScholiaQ62043464MaRDI QIDQ1729699

Luigi Ambrosio, Dario Trevisan, Federico Stra

Publication date: 28 February 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04960

zbMATH Keywords

optimal transportgeometric probabilityminimal matching

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Matching models (91B68) Optimal transportation (49Q22)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Heat kernel bounds on metric measure spaces and some applications
• Optimal transport from Lebesgue to Poisson
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• On the rate of convergence in Wasserstein distance of the empirical measure
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Equivalent semigroup properties for the curvature-dimension condition
• Minimax grid matching and empirical measures
• Duality on gradient estimates and Wasserstein controls
• On optimal matchings
• Matching random samples in many dimensions
• The transportation cost from the uniform measure to the empirical measure in dimension \(\geq 3\)
• Asymptotics for transportation cost in high dimensions
• Probability theory of classical Euclidean optimization problems
• Almost sure convergence of the minimum bipartite matching functional in Euclidean space
• Limit theorems for random normalized distortion
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• On optimal matching of Gaussian samples
• On the stochastic convergence of representations based on Wasserstein metrics
• Curvature and the eigenvalues of the Laplacian
• Analysis for Diffusion Processes on Riemannian Manifolds
• Combinatorial Optimization Over Two Random Point Sets
• The Trace of the Heat Kernel in Lipschitz Domains
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• A Topological Application of the Isoperimetric Inequality
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• Analysis and Geometry of Markov Diffusion Operators
• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• Upper and Lower Bounds for Stochastic Processes
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Semicontinuity problems in the calculus of variations
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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