Discrepancy and Fisher information

Gleb Smirnov; Roman Vershynin

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arXiv · 2605.13107

Discrepancy and Fisher information

Gleb Smirnov·Roman Vershynin

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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.

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Gleb Smirnov, Roman Vershynin. 2026-05-13. Discrepancy and Fisher information. https://arxiv.org/abs/2605.13107

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