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

References in corpus (2)

• A Frostman type lemma for sets with large intersections, and an application to Diophantine approximation
• Hausdorff dimension of affine random covering sets in torus

Cited by in corpus (8)

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• Dimensions of random covering sets in Riemann manifolds
• Random Covering Sets in Metric Space with Exponentially Mixing Property
• Hausdorff dimension of limsup sets of rectangles in the Heisenberg group
• Projections of random covering sets
• Hausdorff dimension of random limsup sets of balls in the unit cube
• On Shrinking Targets for Piecewise Expanding Interval Maps