Irregularity of distribution in Wasserstein distance

2019/10/30 by Graham, Cole · 1 citation
#11K06 #11K38 #42A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.14181

Abstract

We study the non-uniformity of probability measures on the interval and the circle. On the interval, we identify the Wasserstein-p distance with the classical L^p-discrepancy. We thereby derive sharp estimates in Wasserstein distances for the irregularity of distribution of sequences on the interval and the circle. Furthermore, we prove an L^p-adapted Erdős-Turán inequality.

Cited by

• Random walks and quadratic number fields

Related

• Wasserstein Distance, Fourier Series and Applications
• Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences
• Stein's Method for Probability Distributions on \mathbbS¹
• Weak convergence of empirical Wasserstein type distances
• Bounding Kolmogorov distances through Wasserstein and related integral probability metrics