For random subsequences of the rotation {nα}, the expected p-Wasserstein distance of the empirical measure to uniformity decays like n^{-1/2}, (log n)^{1-1/(p∨2)} n^{-1/2}, or n^{-1/(βγ)} depending on whether βγ<2, =2, or >2.
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Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$
For random subsequences of the rotation {nα}, the expected p-Wasserstein distance of the empirical measure to uniformity decays like n^{-1/2}, (log n)^{1-1/(p∨2)} n^{-1/2}, or n^{-1/(βγ)} depending on whether βγ<2, =2, or >2.