2505.11721
Variational Principles for Hausdorff and Packing Dimensions of Fractal Percolation on Self-Affine Sponges
Julien Barral, Guilhem Brunet
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper establishes Hausdorff and packing variational principles for statistically self-affine sponges via inhomogeneous Mandelbrot measures of type ℓ and a large-deviation/covering framework tailored to anisotropic Lyapunov exponents. The candidate solution instead proves a self-similar-style s_* formula from a one-parameter pressure Q(s) using Lipschitz radii r_i and a ratio H/χ law for IMMs; this ignores the multi-directional (self-affine) structure and fails to match the paper’s main results or methods.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper gives rigorous variational principles for Hausdorff and packing dimensions in the random self-affine setting, leveraging a refined IMM framework and large-deviation estimates near q=1, together with Lyapunov-adapted coverings. The results are timely and connect to open phenomena such as dimensional gaps in sponges. The exposition is solid; minor improvements could further ease navigation through technical sections.