Euclidean random matching in 2D for non-constant densities

DOI10.1007/s10955-020-02608-xzbMath1458.60020arXiv1911.10523OpenAlexW2991150450WikidataQ114225343 ScholiaQ114225343MaRDI QIDQ2659292

Dario Benedetto, Emanuele Caglioti

Publication date: 26 March 2021

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.10523

zbMATH Keywords

Monge-Ampère equationoptimal transportempirical measuresEuclidean matching

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Related Items (6)

On the quadratic random matching problem in two-dimensional domains ⋮ Convergence of asymptotic costs for random Euclidean matching problems ⋮ $k$-Variance: A Clustered Notion of Variance ⋮ Optimal Matching of Random Samples and Rates of Convergence of Empirical Measures ⋮ Optimal transport methods for combinatorial optimization over two random point sets ⋮ Random assignment problems on \(2d\) manifolds

Cites Work

• On optimal matchings
• Matching random samples in many dimensions
• Asymptotics for transportation cost in high dimensions
• Scaling and non-standard matching theorems
• Remarks on the Monge-Kantorovich problem in the discrete setting
• A PDE approach to a 2-dimensional matching problem
• Anomalous scaling of the optimal cost in the one-dimensional random assignment problem
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Finer estimates on the \(2\)-dimensional matching problem
• On the optimal map in the 2-dimensional random matching problem
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Uniformly elliptic Liouville type equations: concentration compactness and a priori estimates
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• Comparison between W₂ distance and Ḣ⁻¹ norm, and Localization of Wasserstein distance

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