Self-affine sponges with random contractions
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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Fixed Point Theorems Analysis
Geometry and complex manifolds
Publication details
- Journal / source
- Probability Theory and Related Fields
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 15 June 2026
- Language
- EN