Random trial examines Hausdorff dimension of Cantor sets with overlaps, indicating new dimensions of mathematical study.
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.
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Lai et al. (2026) studied this question.
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