Discrepancy and Fisher information
Probability
2026-05-14 v1
Abstract
We give an online algorithm that keeps a symmetric random walk inside a convex body by discarding some of its steps. The expected number of discarded steps is controlled by a Fisher-information-type quantity associated with the body. For the cube, this gives a dimension-free bound: a walk with unit Euclidean steps can be kept bounded in all coordinates while discarding only a small constant fraction of the steps on average.
Cite
@article{arxiv.2605.13107,
title = {Discrepancy and Fisher information},
author = {Gleb Smirnov and Roman Vershynin},
journal= {arXiv preprint arXiv:2605.13107},
year = {2026}
}