English

Self-affine sponges with random contractions

Dynamical Systems 2025-05-08 v1 Probability

Abstract

We compute the almost sure Hausdorff dimension of random self-affine sponges in Rd\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.

Keywords

Cite

@article{arxiv.2505.04383,
  title  = {Self-affine sponges with random contractions},
  author = {Balázs Bárány and Antti Käenmäki and Michał Rams},
  journal= {arXiv preprint arXiv:2505.04383},
  year   = {2025}
}

Comments

24 pages, 7 figures

R2 v1 2026-06-28T23:24:26.164Z