Random covering sets in metric space with exponentially mixing property

Authors：Hu, Zhang-nan; Li, Bing^*

Source：STATISTICS & PROBABILITY LETTERS, 2021, 168: 108922.

DOI：10.1016/j.spl.2020.108922

• Random covering sets
• Exponentially mixing
• Dynamical system
• Metric space
• Huasdorff dimension

Let {B(xi(n), r(n))}(n >= 1) be a sequence of random balls whose centers {xi(n)}(n >= 1) is a stationary process, and {r(n)}(n >= 1) is a sequence of positive numbers decreasing to 0. Our object is the random covering set E = lim sup(n ->infinity) B(xi(n), r(n)), that is, the points covered by B(xi(n), r(n)) infinitely often. The sizes of E are investigated from the viewpoint of measure, dimension and topology.