2022/04/12 by Michael A. Klatt, Klatt, Michael A., Steffen Winter +1 · 1 citation
Mathematics · Physics and Astronomy · #28A80 #60K35 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2204.05878
openalex publication_date 2022/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine almost sure limits of rescaled intrinsic volumes of the construction steps of fractal percolation in ℝd for any dimension d≥ 1. We observe a factorization of these limit variables which allows, in particular, to determine their expectations and covariance structure. We also show convergence of rescaled expectations and variances of the intrinsic volumes of the construction steps to expectations and variances of the limit variables and give rates for this convergence in some cases. These results significantly extend our previous work that addressed only limits of expectations of intrinsic volumes.