A Note on Random Coverings of Tori

Abstract

This note provides a generalisation of a recent result by Järvenpää, Järvenpää, Koivusalo, Li, and Suomala, (to appear), on the dimension of limsup-sets of random coverings of tori. The result in this note is stronger in the sense that it provides also a large intersection property of the limsup-sets, the assumptions are weaker, and it implies the result of Järvenpää, Järvenpää, Koivusalo, Li, and Suomala as a special case. The proof is based on a recent result by Persson and Reeve from 2013.

4 pages, The definitions of E_k and mu_k have been corrected