@misc{9226080,
  abstract     = {{We review groups acting on rooted trees and discuss their topological and measure-theoretic structure as compact topological groups using the theory of profinite groups and Haar measures.
We introduce new notions of fractal-like structures for groups acting on rooted trees: shifted fractality and shifted super strong fractality, as generalisations of fractality and super strong fractality.
These new notions generalise measure-theoretic results regarding the pushforward of measures and probabilistic independence.
Furthermore, we review the fixed-point process, fixed-point proportion, and application of martingale processes in this context.
We apply these theories to show that the fixed-point proportion of a level transitive shifted super-strongly fractal group acting on a bounded tree is zero; this gives a natural extension to the analogous result for super-strongly fractal groups.}},
  author       = {{Sukkumnoed, Danthai}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{Fixed-point Proportion of Groups Acting on Rooted Trees}},
  year         = {{2026}},
}