A SIMPLE FOURIER ANALYTIC PROOF OF THE AKT OPTIMAL MATCHING THEOREM

• 成果类型: Article
• 署名作者: Bobkov, Sergey G.; Ledoux, Michel
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1656
• 发表日期: 2021
• 页码: 2567-2584
• 关键词: distance

摘要

We present a short and elementary proof of the Ajtai-Komlos-Tusnady (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.