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Level-Transitive Groups with Positive Fixed-Point Proportion and Hausdorff Dimension

A method to explicitly compute the fixed-point proportion of any iterated wreath product acting on a d-regular rooted tree (and a non-group generalization), used to construct a family of self-similar, level-transitive, finite-type depth-2 groups (d >= 3, d != 2 mod 4) with positive Hausdorff dimension and positive, explicitly calculable fixed-point proportion; the iterated Galois group of x^d + 1 arises in the family.