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- W4318906099 abstract "Average distance between two points in a unit-volume body $K subset mathbb{R}^n$ tends to infinity as $n to infty$. However, for two small subsets of volume $varepsilon > 0$ the situation is different. For unit-volume cubes and euclidean balls the largest distance is of order $sqrt{-ln varepsilon}$, for simplexes and hyperoctahedrons $-$ of order $-ln varepsilon$, for $ell_p$ balls with $p in [1;2]$ $-$ of order $(-ln varepsilon)^{frac{1}{p}}$. These estimates are not dependent on the dimensionality $n$. The goal of the paper is to study this phenomenon. Isoperimetric inequalities will play a key role in our approach." @default.
- W4318906099 created "2023-02-03" @default.
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- W4318906099 date "2023-01-31" @default.
- W4318906099 modified "2023-09-27" @default.
- W4318906099 title "Dimension-free estimates on distances between subsets of volume $varepsilon$ inside a unit-volume body" @default.
- W4318906099 doi "https://doi.org/10.48550/arxiv.2301.13495" @default.
- W4318906099 hasPublicationYear "2023" @default.
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