2025/05/07 by Jan Rataj, Rataj, Jan, Steffen Winter +3
Computer Science · Mathematics · #53C65 #60D05 #60G57 #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Primary 28A80 #Probability (math.PR) #Secondary 28A75 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2505.04801
openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a class of random self-similar fractals based on code trees which includes random recursive, homogeneous and V-variable fractals and many more. For such random fractals we consider mean values of the Lipschitz-Killing curvatures of their parallel sets for small parallel radii. Under the uniform strong open set condition and some further geometric assumptions we show that rescaled limits of these mean values exist as the parallel radius tends to 0. Moreover, integral representations are derived for these limits which recover and extend those known in the deterministic case and certain random cases. Results on the mean Minkowski content are included as a special case and shown to hold under weaker geometric assumptions.