On $μ$-Dvoretzky random covering of the circle

Dvoretzky覆盖中的未覆盖集是一个重数集

The non-covered set in Dvoretzky covering is a set of multiplicity

该研究证明Dvoretzky随机覆盖中的未覆盖集是重数集，方法是证明自然乘法混沌测度为Rajchman测度。

Dvoretzky随机覆盖的Salem性质

Salem properties of Dvoretzky random coverings

本文研究了Dvoretzky随机覆盖中未覆盖集合的Salem性质，通过建立相关性质来探讨其数学特征。

On genericity of non-uniform Dvoretzky coverings of the circle

The classical Dvoretzky covering problem asks for conditions on the sequence of lengths $\{\ell_n\}_{n\in \mathbb{N}}$ so that the random intervals $I_n : = (ω_n -(\ell_n/2), ω_n +(\ell_n/2))$ where $ω_n$ is a sequence of i.i.d. uniformly distributed random variable, covers any point on the circle $\mathbb{T}$ infinitely often. We consider the case when $ω_n$ are absolutely continuous with a density function $f$. When $m_f=essinf_\mathbb{T}f>0$ and the set $K_f$ of its essential infimum points satisfies $\overline{\dim}_\mathrm{B} K_f<1$, where $\overline{\dim}_\mathrm{B}$ is the upper box-cou…

一般测度驱动的Dvoretzky覆盖问题

Dvoretzky covering problem for general measures

本文提出了一般测度驱动的Dvoretzky覆盖问题的解决方案，利用潜在理论和Jankov-von Neumann定理，确定了多项式递减序列的临界指数及临界常数。

均匀圆随机覆盖问题的一些确定结果

Certain results on uniform circle random covering problems

本文扩展了均匀圆随机覆盖问题中来自文献[13]的一个定理。

Dynamical models for circle covering: Brownian motion and Poisson updating

We consider two dynamical variants of Dvoretzky's classical problem of random interval coverings of the unit circle, the latter having been completely solved by L. Shepp. In the first model, the centers of the intervals perform independent Brownian motions and in the second model, the positions of the intervals are updated according to independent Poisson processes where an interval of length $\ell$ is updated at rate $\ell^{-α}$ where $α\ge0$ is a parameter. For the model with Brownian motions, a special case of our results is that if the length of the $n$th interval is $c/n$, then there are …