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arXiv · 1910.08056

On $\mu$-Dvoretzky random covering of the circle

Aihua Fan·Davit Karagulyan
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Abstract

In this paper, we study the Dvoretzky covering problem with non-uniformly distributed centers. When the probability law of the centers admits an absolutely continuous density which satisfies a regular condition on the set of essential infimum points, we give a necessary and sufficient condition for covering the circle. When the lengths of covering intervals are of the form $\ell_n = \frac{c}{n}$, we give a necessary and sufficient condition for covering the circle, without imposing any regularity on the density function.

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Aihua Fan, Davit Karagulyan. 2019-10-17. On $\mu$-Dvoretzky random covering of the circle. https://arxiv.org/abs/1910.08056

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