On the inverse of the star-discrepancy problem

Wednesday, 13th September 2023

Abstract

The star-discrepancy measures how well a point set is distributed in the unit cube with respect to the uniform measure. It plays a role in the construction of uniformly distributed points and pseudo-random number generators. A result from 2001 in Acta Arithmetica by Heinrich et al asserts that there exists a point set with N points in the d dimensional unit cube whose star-discrepancy is bounded by $C \sqrt{d/N}$. The proof is based on concentration of measure and is not constructive. In this talk we discuss how the inverse of the star-discrepancy problem is related to pseudo-random number generators and driver sequences for Markov chain Monte Carlo and discuss recent progress on explicit constructions for similar problems.