Electronic Journal of Probability

Hitting probabilities of random covering sets in tori and metric spaces

Esa Järvenpää, Maarit Järvenpää, Henna Koivusalo, Bing Li, Ville Suomala, and Yimin Xiao

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Abstract

We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the $d$-dimensional torus. In metric spaces, we consider covering sets generated by balls and, in tori, we deal with general analytic generating sets.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 1, 18 pp.

Dates
Received: 22 October 2015
Accepted: 17 May 2016
First available in Project Euclid: 5 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1483585523

Digital Object Identifier
doi:10.1214/16-EJP4658

Mathematical Reviews number (MathSciNet)
MR3613694

Zentralblatt MATH identifier
06681503

Subjects
Primary: 60D05, 28A80

Keywords
random covering set hitting probability dimension of intersection

Rights
Creative Commons Attribution 4.0 International License.

Citation

Järvenpää, Esa; Järvenpää, Maarit; Koivusalo, Henna; Li, Bing; Suomala, Ville; Xiao, Yimin. Hitting probabilities of random covering sets in tori and metric spaces. Electron. J. Probab. 22 (2017), paper no. 1, 18 pp. doi:10.1214/16-EJP4658. https://projecteuclid.org/euclid.ejp/1483585523


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