2021/07/30 by Jan Rataj, Rataj, Jan, Steffen Winter +3 · 1 citation
Computer Science · Mathematics · #53C65 #60D05 #60G57 #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary: 28A80 #Probability (math.PR) #Secondary: 28A75 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2107.14431
openalex publication_date 2021/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. 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 zero. Moreover, integral representations are derived for these limits which extend those known in the deterministic case.