A simple Fourier analytic proof of the AKT optimal matching theorem
نویسندگان
چکیده
We present a short and elementary proof of the Ajtai–Komlós–Tusnády (AKT) optimal matching theorem in dimension 2 via Fourier analysis smoothing argument. The upper bound applies to more general families samples, including dependent variables, interest study rates convergence for empirical measures. Following recent pde approach by L. Ambrosio, F. Stra D. Trevisan, we also adapt simple lower bound.
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ژورنال
عنوان ژورنال: Annals of Applied Probability
سال: 2021
ISSN: ['1050-5164', '2168-8737']
DOI: https://doi.org/10.1214/20-aap1656