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On mu-Dvoretzky random covering of the circle

Abstract : In this paper, we study the Dvoretzky covering problem with non-uniformly distributed centers. When the probability law of the centers is absolutely continuous w.r.t. Lebesgue measure and satisfies a regularity 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 l(n) = 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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https://hal-u-picardie.archives-ouvertes.fr/hal-03621993
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Soumis le : lundi 28 mars 2022 - 16:23:11
Dernière modification le : mercredi 14 septembre 2022 - 17:46:27

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Aihua Fan, Davit Karagulyan. On mu-Dvoretzky random covering of the circle. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2021, 27 (2), pp.1270-1290. ⟨10.3150/20-BEJ1273⟩. ⟨hal-03621993⟩

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