On randomly placed arcs on the circle

TL;DR

This paper characterizes the size and intersection properties of points on a circle covered infinitely often by a sequence of random arcs, using Hausdorff measures.

Contribution

It provides a complete description of the measure and intersection properties of the set of points covered infinitely often by random arcs on the circle.

Findings

The set of points covered infinitely often has a specific Hausdorff measure.

This set is shown to be a set with large intersection.

The results give a precise measure-theoretic description of the coverage.

Abstract

We completely describe in terms of Hausdorff measures the size of the set of points of the circle that are covered infinitely often by a sequence of random arcs with given lengths. We also show that this set is a set with large intersection.