On the covering by small random intervals.
type: Item
instance of: scholarly article
title: On the covering by small random intervals.
zbMATH Open document ID: 1037.60010
author: Jun Wu
author: Ai-Hua Fan
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2004-03-15T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77794
review text: Let \(a>0\) and \(\alpha >1\), and for each \(n\geq 0\), let \(\ell_n=a/n^{\alpha}\). If \((w_n)_{n\geq 0}\) is a sequence of independent random variables uniformly distributed over the unit interval \([0,1)\) and if for each \(n\), we set \(I_n=w_n+(0,\ell_n)\) (modulo 1), then \((I_n)_{n\geq 0}\) is a sequence of random intervals. The authors consider the set \(E_{\infty}(w)=\limsup I_n\) of points in the unit interval which are covered infinitely often, and they show that the Hausdorff dimension of this set is almost surely equal to \(1/\alpha\).
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 2057149
zbMATH Keywords: random covering
zbMATH Keywords: uniform sample spacing
zbMATH Keywords: Hausdorff dimension
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
OpenAlex ID: W2063333818
DOI: 10.1016/J.ANIHPB.2003.07.001
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description: scientific article; zbMATH DE number 2057149