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arXiv · 1909.06193

A simple Fourier analytic proof of the AKT optimal matching theorem

Sergey Bobkov·Michel Ledoux
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Abstract

We present a short and elementary proof of the Ajtai-Koml\'os-Tusn\'ady (AKT) optimal matching theorem in dimension 2 via Fourier analysis and a smoothing argument. The upper bound applies to more general families of samples, including dependent variables, of interest in the study of rates of convergence for empirical measures. Following the recent pde approach by L. Ambrosio, F. Stra and D. Trevisan, we also adapt a simple proof of the lower bound.

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Sergey Bobkov, Michel Ledoux. 2019-09-13. A simple Fourier analytic proof of the AKT optimal matching theorem. https://arxiv.org/abs/1909.06193

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