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- W4287286075 abstract "Motivated by the random covering problem and the study of Dirichlet uniform approximable numbers, we investigate the uniform random covering problem. Precisely, consider an i.i.d. sequence $omega=(omega_n)_{ngeq 1}$ uniformly distributed on the unit circle $mathbb{T}$ and a sequence $(r_n)_{ngeq 1}$ of positive real numbers with limit $0$. We investigate the size of the random set [ mathcal U (omega):={yin mathbb{T}: forall Ngg 1, exists n leq N, text{s.t.} | omega_n -y | < r_N }. ] Some sufficient conditions for $mathcal U(omega)$ to be almost surely the whole space, of full Lebesgue measure, or countable, are given. In the case that $mathcal U(omega)$ is a Lebesgue null measure set, we provide some estimations for the upper and lower bounds of Hausdorff dimension." @default.
- W4287286075 created "2022-07-25" @default.
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- W4287286075 date "2021-03-02" @default.
- W4287286075 modified "2023-10-09" @default.
- W4287286075 title "Uniform random covering problems" @default.
- W4287286075 doi "https://doi.org/10.48550/arxiv.2103.01595" @default.
- W4287286075 hasPublicationYear "2021" @default.
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