Asymptotics for transportation cost in high dimensions

DOI10.1007/BF02213456zbMath0811.60022MaRDI QIDQ1345081

V. Pereyra

Publication date: 26 February 1995

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

zbMATH Keywords

Poisson point processesstrong limit theoremspermutations of the integersoptimal bipartite matching

Mathematics Subject Classification ID

Strong limit theorems (60F15) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (36)

Convergence of asymptotic costs for random Euclidean matching problems ⋮ Some recent developments in functional inequalities ⋮ Parametrization of Random Vectors in Polynomial Chaos Expansions via Optimal Transportation ⋮ Limit laws of the empirical Wasserstein distance: Gaussian distributions ⋮ Approximation by finitely supported measures ⋮ Kac's program in kinetic theory ⋮ Euclidean random matching in 2D for non-constant densities ⋮ Constructive quantization: approximation by empirical measures ⋮ The empirical cost of optimal incomplete transportation ⋮ $k$-Variance: A Clustered Notion of Variance ⋮ Optimal Matching of Random Samples and Rates of Convergence of Empirical Measures ⋮ Density estimation of multivariate samples using Wasserstein distance ⋮ A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling ⋮ The Wasserstein distance to the circular law ⋮ Limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds ⋮ Asymptotics for Strassen's optimal transport problem ⋮ Optimal transport methods for combinatorial optimization over two random point sets ⋮ Rates of convergence for partial mass problems ⋮ Behavior of the empirical Wasserstein distance in \({\mathbb R}^d\) under moment conditions ⋮ On the mean speed of convergence of empirical and occupation measures in Wasserstein distance ⋮ A PDE approach to a 2-dimensional matching problem ⋮ Gravitational allocation for uniform points on the sphere ⋮ On the rate of convergence in Wasserstein distance of the empirical measure ⋮ Rate of convergence of bootstrapped empirical measures ⋮ On Kac's chaos and related problems ⋮ An algorithm to approximate the optimal expected inner product of two vectors with given marginals ⋮ Some results on the optimal matching problem for the Jacobi model ⋮ WASSERSTEIN DISTANCES FOR VORTICES APPROXIMATION OF EULER-TYPE EQUATIONS ⋮ On optimal matching of Gaussian samples ⋮ Generalization error of GAN from the discriminator's perspective ⋮ Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance ⋮ One-dimensional empirical measures, order statistics, and Kantorovich transport distances ⋮ Finer estimates on the \(2\)-dimensional matching problem ⋮ Robust clustering tools based on optimal transportation ⋮ Combinatorial Optimization Over Two Random Point Sets ⋮ A review of the mean field limits for Vlasov equations

Cites Work

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• On optimal matchings
• The average-case analysis of some on-line algorithms for bin packing
• Growth rates of Euclidean minimal spanning trees with power weighted edges
• Subadditive Euclidean functionals and nonlinear growth in geometric probability
• Matching random samples in many dimensions
• Rates of convergence of means for distance-minimizing subadditive Euclidean functionals
• Limit theorems and rates of convergence for Euclidean functionals
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Matching Theorems and Empirical Discrepancy Computations using Majorizing Measures
• The Speed of Mean Glivenko-Cantelli Convergence

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