On $\mu$-Dvoretzky random covering of the circle
Probability
2021-11-02 v1 Classical Analysis and ODEs
Dynamical Systems
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 , we give a necessary and sufficient condition for covering the circle, without imposing any regularity on the density function.
Keywords
Cite
@article{arxiv.1910.08056,
title = {On $\mu$-Dvoretzky random covering of the circle},
author = {Aihua Fan and Davit Karagulyan},
journal= {arXiv preprint arXiv:1910.08056},
year = {2021}
}
Comments
19 pages