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Wasserstein Distance, Fourier Series and Applications
[article]
2020
arXiv
pre-print
We study the Wasserstein metric W_p, a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance W_1 between the distribution of quadratic residues in a finite field 𝔽_p and uniform distribution by ≲ p^-1/2 (the Polya-Vinogradov inequality implies ≲ p^-1/2logp). We also show for continuous f:𝕋→ℝ_ with mean value 0 ( f) ·( ∑_k=1^∞ |f̂(k)|^2/k^2)^1/2≳f^2_L^1(𝕋)/f_L^∞(𝕋). Moreover,
arXiv:1803.08011v3
fatcat:mw2lvnuqubfrdibmtskavks6de