Statistically self-affine sets: Hausdorff and box dimensions

DOI10.1007/BF02214277zbMath0803.60011MaRDI QIDQ1322917

Steven P. Lalley, Dimitrios Gatzouras

Publication date: 3 January 1995

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensionbox dimensionBouligand-Minkowski dimensionsbranching processes in random environmentgeneralized Sierpinski carpetsstatistically self-affine

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Fractals (28A80) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (12)

Dimensions of random statistically self-affine Sierpinski sponges in \(\mathbb{R}^k\) ⋮ Box-counting dimension and differentiability of box-like statistically self-affine functions ⋮ The Assouad dimension of randomly generated fractals ⋮ Dimensions of random affine code tree fractals ⋮ The Assouad spectrum of random self-affine carpets ⋮ The box-counting dimension of random box-like self-affine sets ⋮ HAUSDORFF DIMENSION OF CERTAIN RANDOM SELF-AFFINE FRACTALS ⋮ RANDOM SUBSETS OF SELF‐AFFINE FRACTALS ⋮ The Mass Transference Principle: Ten years on ⋮ Variational formula related to the self-affine Sierpinski carpets ⋮ Dimension and measure for typical random fractals ⋮ The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group

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• On Branching Processes with Random Environments: I: Extinction Probabilities
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