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Self-affine sponges with random contractions

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arxiv 2505.04383 v2 pith:6U3MD6C7 submitted 2025-05-07 math.DS math.PR

Balázs Bárány , Antti Käenmäki , Micha{l} Rams This is my paper · ORCID
classification math.DSmath.PR
keywords randomself-affinespongesaffinealmostarisescomputeconditions
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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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  1. On the Fourier transform of random Bernoulli convolutions

    math.DS 2025-07 accept novelty 7.0 of 10

    For random Bernoulli convolutions, the Fourier transform is in L^1 almost surely whenever λ_g > 2/π, giving absolute continuity and non-empty interior; polynomial Fourier decay holds for every λ_g.

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