A class of random Cantor sets. (English) Zbl 1384.28012

Author’s abstract: In this paper we study a class of random Cantor sets. We determine their almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological point of view, we also compute their typical dimensions in the sense of Baire category. For the natural random measures on these random Cantor sets, we consider their almost sure lower and upper local dimensions. In the end we study the hitting probabilities of a special subclass of these random Cantor sets.


28A80 Fractals
37F40 Geometric limits in holomorphic dynamics
60D05 Geometric probability and stochastic geometry
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