Year: 2026
Type: preprint
Abstract: In this note we present a dimension formula for certain randomized self-similar sets. The self-similar sets we are considering are $d$-dimensional generalizations of rational projections of inhomogeneous sponges: they have overlaps, but the overlapping structure is in some sense well-organized. The randomization happens according to a labelled Galton-Watson tree corresponding to the cylinders of the IFS, for example as in the case of the Mandelbrot percolation set. The dimension formula is given in terms of a pressure function corresponding to the expectation matrices, which describes the overlapping structure and the randomness of the system.
Source: arXiv (Cornell University)
Authors: Orgoványi, Vilma, Simon, Károly
Institution: Budapest University of Technology and Economics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2774216544, G4042934884, G8528715892
OpenAlex ID: W7220936548