2022/01/06 by Yevgeniy Kovchegov, Kovchegov, Yevgeniy, Guochen Xu +3
Mathematics · Physics and Astronomy · #60G18 #60J80 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2201.01899
openalex publication_date 2022/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.