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تسجيل مستخدم جديدOn the rate of convergence of empirical measure in $infty-$Wasserstein distance for unbounded density function
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We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $infty-$Wasserstein distance between the empirical measure of the samples and the true distribution, which extends the previous convergence result by Trilllos and Slepv{c}ev to the case that the true distribution has an unbounded density.
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