Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 625-633
South China University of Technology, Department of Mathematics
Guangzhou, 510641, P.R. China; and
University of Oulu, Department of Mathematical Sciences
P.O. Box 3000, 90014 University of Oulu, Finland;
libing0826 'at' gmail.com
University of Oulu, Department of Mathematical Sciences
P.O. Box 3000, 90014 University of Oulu, Finland;
ville.suomala 'at' oulu.fi
Abstract. Let E = lim supn \to\infty(gn + \xin) be the random covering set on the torus Td, where {gn} is a sequence of ball-like sets and \xin is a sequence of independent random variables uniformly distributed on Td. We prove that E \cap F \neq \emptyset almost surely whenever F\subset Td is an analytic set with Hausdorff dimension, dimH(F) > d - \alpha, where \alpha is the almost sure Hausdorff dimension of E. Moreover, examples are given to show that the condition on dimH(F) cannot be replaced by the packing dimension of F.
2010 Mathematics Subject Classification: Primary 60D05, 28A78, 28A80.
Key words: Random covering sets, hitting probability, Hausdorff dimension.
Reference to this article: B. Li and V. Suomala: A note on the hitting probabilities of random covering sets. Ann. Acad. Sci. Fenn. Math. 39 (2014), 625-633.
doi:10.5186/aasfm.2014.3927
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