Discrepancy and Fisher information
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911679640502272 |
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| author | Smirnov, Gleb Vershynin, Roman |
| author_facet | Smirnov, Gleb Vershynin, Roman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrepancy and Fisher information Smirnov, Gleb Vershynin, Roman Probability 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. |
| title | Discrepancy and Fisher information |
| topic | Probability |
| url | https://arxiv.org/abs/2605.13107 |