A note on uniform random covering problems in metric spaces
Abstract
In this paper, we study the uniform random covering problem in general metric space $(X,d)$. Let $ω=(ω_n)_{n\in\mathbb N}$ be a sequence of independent identically distributed random variables on $(X,μ)$, and $\ell=(\ell_n)_{n\in\mathbb N}$ a sequence of positive real numbers. We analyze the size of the set \[\mathcal{U}(ω,\ell)=\left\{y\in X\colon \forall N\gg1,~\exists 1\le n\le N,~s.t. ~d(ω_n,y)
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Stochastic processes and statistical mechanics
p-Adic Analysis and Mathematical Physics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 February 2026
- Language
- EN
- Document type
- Preprint