Hitting probabilities of random covering sets in tori and metric spaces

Järvenpää, Esa; Järvenpää, Maarit; Koivusalo, Henna; Li, Bing; Suomala, Ville; Xiao, Yimin (2017-01-05)
 
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https://doi.org/10.1214/16-EJP4658

Järvenpää, Esa
Järvenpää, Maarit
Koivusalo, Henna
Li, Bing
Suomala, Ville
Xiao, Yimin
Institute of Mathematical Statistics
05.01.2017

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. http://projecteuclid.org/euclid.ejp/1483585523

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doi:https://doi.org/10.1214/16-EJP4658
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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.

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