A note on random coverings of tori

dina mulyani;

This note provides a generalization of a recent result by J¨arvenp¨a¨a, J¨arvenp¨a¨a, 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 J¨arvenp¨a¨a, J¨arvenp¨a¨a, Koivusalo, Li, and Suomala as a special case. The proof is based on a recent result by Persson and Reeve from 2013.