University of Oulu

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.

Hitting probabilities of random covering sets in tori and metric spaces

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Author: Järvenpää, Esa1; Järvenpää, Maarit1; Koivusalo, Henna2;
Organizations: 1Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland
2Department on Mathematics, University of York, York YO10 5DD, Great Britain
3School of Mathematics, South China University of Technology, Guangzhou, 510641, P. R. China
4Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing MI48824, USA
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Institute of Mathematical Statistics, 2017
Publish Date: 2017-02-09


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.

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Series: Electronic journal of probability
ISSN: 1083-6489
ISSN-E: 1083-6489
ISSN-L: 1083-6489
Volume: 22
Pages: 1 - 18
Article number: 1
DOI: 10.1214/16-EJP4658
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: We acknowledge the support of the Academy of Finland, the Centre of Excellence in Analysis and Dynamics Research. HK thanks the support of EPSRC Grant EP/L001462 and Osk. Huttunen foundation. BL was supported by NSFC 11671151 and 11201155, Guangdong Natural Science Foundation 2014A030313230 and “Fundamental Research Funds for the Central Universities” SCUT (2015ZZ055). YX was supported in part by NSF grants DMS-1307470 and DMS-1309856
Copyright information: Creative Commons Attribution 4.0 International License.