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<p>We compute the almost sure Hausdorff dimension of random self-affine sponges in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Self-affine sponges with random contractions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月15日

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  • Balázs Bárány,
  • Antti Käenmäki,
  • Michał Rams

摘要

We compute the almost sure Hausdorff dimension of random self-affine sponges in \(\mathbb {R}^d\) 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.