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arXiv · 2505.04383

Self-affine sponges with random contractions

Balázs Bárány·Antti Käenmäki·Michał Rams
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Abstract

We compute the almost sure Hausdorff dimension of random self-affine sponges in $\mathbb{R}^d$ without imposing any separation conditions. In this context, randomness arises from the matrices in the defining semigroup, which are random yet the corresponding affine maps share a fixed point.

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Balázs Bárány, Antti Käenmäki, Michał Rams. 2025-05-07. Self-affine sponges with random contractions. https://arxiv.org/abs/2505.04383

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