On the quadratic random matching problem in two-dimensional domains

DOI10.1214/22-EJP784zbMath1487.60017arXiv2110.14372OpenAlexW3209192965MaRDI QIDQ2136099

Dario Trevisan, Michael Goldman, Luigi Ambrosio

Publication date: 10 May 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.14372

zbMATH Keywords

matching problemoptimal transportgeometric probability

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Linear programming (90C05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Functional inequalities, including subadditivity, convexity, etc. (39B62) (L^p)-limit theorems (60F25) Optimal transportation (49Q22)

Related Items (3)

Optimal Matching of Random Samples and Rates of Convergence of Empirical Measures ⋮ Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology ⋮ Optimal transport methods for combinatorial optimization over two random point sets

Uses Software

• Wasserstein GAN

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constructive quantization: approximation by empirical measures
• Boundary regularity of maps with convex potentials. II
• A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions
• On optimal matchings
• Matching random samples in many dimensions
• Tight bounds for minimax grid matching with applications to the average case analysis of algorithms
• Probability theory of classical Euclidean optimization problems
• Asymptotics for weighted minimal spanning trees on random points
• Scaling and non-standard matching theorems
• A PDE approach to a 2-dimensional matching problem
• Anomalous scaling of the optimal cost in the one-dimensional random assignment problem
• Asymptotics for the Euclidean TSP with power weighted edges
• Asymptotics for Euclidean functionals with power-weighted edges
• A generalization of Caffarelli's contraction theorem via (reverse) heat flow
• Random assignment problems on \(2d\) manifolds
• A fluctuation result for the displacement in the optimal matching problem
• Convergence of asymptotic costs for random Euclidean matching problems
• Exact rate of convergence of the expected \(W_2\) distance between the empirical and true Gaussian distribution
• Local laws and rigidity for Coulomb gases at any temperature
• 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
• On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
• Euclidean random matching in 2D for non-constant densities
• The Euclidean Matching Problem
• Combinatorial Optimization Over Two Random Point Sets
• Bayesian Mechanism Design
• Quantitative Linearization Results for the <scp>Monge‐Ampère</scp> Equation
• On the Rate of Convergence of Empirical Measures in ∞-transportation Distance
• Information, Physics, and Computation
• Sobolev met Poincaré
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• Comparison between W₂ distance and Ḣ⁻¹ norm, and Localization of Wasserstein distance
• Upper and Lower Bounds for Stochastic Processes

This page was built for publication: On the quadratic random matching problem in two-dimensional domains