## Electronic Journal of Probability

### Hitting probabilities of random covering sets in tori and metric spaces

#### 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
Accepted: 17 May 2016
First available in Project Euclid: 5 January 2017

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

#### 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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