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On the fixed-point proportion of self-similar groups

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arxiv 2503.00185 v1 pith:QE2QOAIT submitted 2025-02-28 math.GR

Jorge Fariña-Asategui , Santiago Radi This is my paper · ORCID
classification math.GR
keywords groupsfixed-pointproportionself-similaractingapproachauthorcomplex
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We prove that super strongly fractal groups acting on regular rooted trees have null fixed-point proportion. In particular, we show that the fixed-point proportion of an infinite family of iterated monodromy groups of exceptional complex polynomials have the same property. The proof uses the approach of Rafe Jones in [15] based on martingales and a recent result of the first author on the dynamics of self-similar groups [6].

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weakly branch actions: first-order theory, rigidity and Boston's conjecture

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  5. Random subgroups of branch groups

    math.GR 2025-08 conditional novelty 6.0 of 10

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