Exact packing dimension of random self-similar sests

TL;DR

This paper extends the understanding of the exact packing dimension of random self-similar sets by removing restrictive assumptions on diameter reduction ratios, broadening applicability.

Contribution

It generalizes previous results by allowing variable diameter reduction ratios in random recursive constructions.

Findings

Established the exact packing dimension under more general conditions.

Removed the assumption of constant or zero diameter reduction ratios.

Extended the theoretical framework for random self-similar sets.

Abstract

We extend the results previously published on exact packing dimensions of random recursive constructions to include constructions satisfying commonly occurring conditions. We remove the restrictive assumption that the diameter reduction ratios between the offsping are either constant almost surely, or 0.