Hausdorff dimension of random limsup sets of balls in the unit cube
Fredrik Ekstr\"om
TL;DR
This paper provides a new proof for the formula determining the Hausdorff dimension of points covered infinitely often by a sequence of randomly distributed balls in the unit cube, linking it to the sizes of these balls.
Contribution
It introduces a novel proof technique for the Hausdorff dimension formula of random limsup sets of balls in the unit cube.
Findings
The Hausdorff dimension can be explicitly calculated based on the sizes of the balls.
The new proof simplifies understanding of the dimension formula.
The result applies to sequences of randomly distributed balls in the unit cube.
Abstract
The Hausdorff dimension of the set of points that are covered infinitely many times by a sequence of randomly distributed balls in the unit cube can be expressed in terms of the sizes of the balls. This note presents a new proof of the formula.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Computational Geometry and Mesh Generation