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arXiv · 2610.08465

Dimension properties of a family of random self-similar iterated function systems

Vilma Orgoványi·Károly Simon
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Abstract

In this note we present a dimension formula for certain randomized self-similar sets. The self-similar sets we are considering are $d$-dimensional generalizations of rational projections of inhomogeneous sponges: they have overlaps, but the overlapping structure is in some sense well-organized. The randomization happens according to a labelled Galton-Watson tree corresponding to the cylinders of the IFS, for example as in the case of the Mandelbrot percolation set. The dimension formula is given in terms of a pressure function corresponding to the expectation matrices, which describes the overlapping structure and the randomness of the system.

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Vilma Orgoványi, Károly Simon. 2026-10-06. Dimension properties of a family of random self-similar iterated function systems. https://arxiv.org/abs/2610.08465

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