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 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.
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