Random sets are close to low-discrepancy sets
arXiv:2607.12263
summary
The paper proves that a random sample from any probability distribution in ℝⁿ can be slightly adjusted to become a low‑discrepancy point set with star discrepancy roughly polylog(n)/n.
Abstract
We show that a random sample from an arbitrary probability measure on is close to a low-discrepancy point set. Namely, after moving only a small fraction of the sample points in expectation, one obtains an -point set with star discrepancy with respect to the original measure.
10 pages
Topics & keywords
#discrepancy theory#random sampling#geometric probability#high-dimensional geometry#approximationstar discrepancypolylogarithmic boundpoint set adjustmentprobability measure