The quasi-Assouad dimension for stochastically self-similar sets

Abstract

The class of stochastically self-similar sets contains many famous examples of random sets, e.g. Mandelbrot percolation and general fractal percolation. Under the assumption of the uniform open set condition and some mild assumptions on the iterated function systems used, we show that the quasi-Assouad dimension of self-similar random recursive sets is almost surely equal to the almost sure Hausdorff dimension of the set. We further comment on random homogeneous and $V$-variable sets and the removal of overlap conditions.

14 pages

References in corpus (3)

• Weak separation condition, Assouad dimension, and Furstenberg homogeneity
• On the dimensions of attractors of random self-similar graph directed iterated function systems
• Random affine code tree fractals: Hausdorff and affinity dimensions and pressure

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