Description
The Wasserstein metric, a notion originating in optimal transportation, is a metric on the set of Borel probability measures on a complete, separable metric space. As a far reaching generalization of a classical smoothing inequality of Esseen on the real line, in this talk we present a general upper estimate for the Wasserstein metric on a compact, connected Lie group in terms of the Fourier transform of the probability measures. The proof is based on Kantorovich duality and smoothing with a Fejér-like kernel. The result is basically sharp, and has several applications to equidistribution and to random walks on compact groups. As a special case we obtain an Erdős-Turán inequality, estimating the distance of a finite set from uniformity in the Wasserstein metric in terms of character sums.
Zoom link: https://zoom.us/j/99419186220?pwd=dkFXNDBCOXBoR0NoU2dJZjI5Zmt4UT09