Properties of a random Cantor set with overlaps
Number Theory
2026-01-29 v1
Abstract
We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The results extend known formulas to a case where the Open Set Condition fails. Our methodology is based on the theory of expansions in non-integer bases.
Cite
@article{arxiv.2601.20644,
title = {Properties of a random Cantor set with overlaps},
author = {Anna Chiara Lai and Paola Loreti},
journal= {arXiv preprint arXiv:2601.20644},
year = {2026}
}