Invariant Galton-Watson trees: metric properties and attraction with respect to generalized dynamical pruning

Yevgeniy Kovchegov; Guochen Xu; Ilya Zaliapin

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arXiv · 2201.01899

Invariant Galton-Watson trees: metric properties and attraction with respect to generalized dynamical pruning

Yevgeniy Kovchegov·Guochen Xu·Ilya Zaliapin

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Abstract

Invariant Galton-Watson (IGW) tree measures is a one-parameter family of critical Galton-Watson measures invariant with respect to a large class of tree reduction operations. Such operations include the generalized dynamical pruning (also known as hereditary reduction in a real tree setting) that eliminates descendant subtrees according to the value of an arbitrary subtree function that is monotone nondecreasing with respect to an isometry-induced partial tree order. We show that, under a mild regularity condition, the IGW measures are the only attractors of critical Galton-Watson measures with respect to the generalized dynamical pruning. We also derive the distributions of height, length, and size of the IGW trees.

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Yevgeniy Kovchegov, Guochen Xu, Ilya Zaliapin. 2022-01-06. Invariant Galton-Watson trees: metric properties and attraction with respect to generalized dynamical pruning. https://arxiv.org/abs/2201.01899

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