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

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