Optimal Matching Problem on the Boolean Cube

2025/03/20 by Feng, Shi
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.16713

Abstract

We establish upper and lower bounds for the expected Wasserstein distance between the random empirical measure and the uniform measure on the Boolean cube. Our analysis leverages techniques from Fourier analysis, following the framework introduced in \citebobkov2021simple, as well as methods from large deviations theory.

Related

• Bounding quantiles of Wasserstein distance between true and empirical measure
• Optimality of empirical measures as quantizers
• Convergence rate of empirical measures in the subspace robust Wasserstein distance
• Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHS
• A short proof on the rate of convergence of the empirical measure for the Wasserstein distance