论文标题
不变的Galton-Watson树：关于广义动力修剪的公制特性和吸引力
Invariant Galton-Watson trees: metric properties and attraction with respect to generalized dynamical pruning
论文作者
论文摘要
不变的Galton-Watson（IGW）树度量是关键的Galton-Watson的单参数家族，相对于大型的减树作业不变。此类操作包括广义动力学修剪（也称为真实树环境中的遗传性还原），该动态修剪根据均衡性诱导的部分树阶的任意子树函数的值消除了后代子树。我们表明，在轻度的规律性条件下，IGW度量是关键的Galton-Watson量度相对于广义动力学的吸引者。我们还得出了IGW树高度，长度和大小的分布。
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.
