Open Access
2017 Hitting probabilities of random covering sets in tori and metric spaces
Esa Järvenpää, Maarit Järvenpää, Henna Koivusalo, Bing Li, Ville Suomala, Yimin Xiao
Electron. J. Probab. 22: 1-18 (2017). DOI: 10.1214/16-EJP4658


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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Esa Järvenpää. Maarit Järvenpää. Henna Koivusalo. Bing Li. Ville Suomala. Yimin Xiao. "Hitting probabilities of random covering sets in tori and metric spaces." Electron. J. Probab. 22 1 - 18, 2017.


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

zbMATH: 06681503
MathSciNet: MR3613694
Digital Object Identifier: 10.1214/16-EJP4658

Primary: 60D05, 28A80

Keywords: dimension of intersection , hitting probability , Random covering set

Vol.22 • 2017
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