2022
DOI: 10.48550/arxiv.2201.02059
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On microsets, Assouad dimension and lower dimension of random fractals, and Furstenberg's homogeneity

Abstract: We study the collection of microsets of randomly constructed fractals, which in this paper, are referred to as Galton-Watson fractals. This is a model that generalizes Mandelbrot percolation, where Galton-Watson trees (whose offspring distribution is not necessarily binomial) are projected to R d by a coding map which arises from an iterated function system (IFS) of similarity maps. We show that for such a random fractal E, whenever the underlying IFS satisfies the open set condition, almost surely the Assouad… Show more

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