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On the distribution of distances between specified nodes in increasing trees

机译：关于递增树中指定节点之间的距离分布

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摘要

We study the quantity distance between nodej and noden in a random tree of sizen chosen from a family of increasing trees. For those subclass of increasing tree families, which can be constructed via a tree evolution process, we give closed formul??for the probability distribution, the expectation and the variance. Furthermore we derive a distributional decomposition of the random variable considered and we show a central limit theorem of this quantity, for arbitrary labels 1 ≤ j < n and n → ∞. Such tree models are of particular interest in applications, e.g., the widely used models of recursive trees, plane-oriented recursive trees and binary increasing trees are special instances and are thus covered by our results.
机译：我们研究了从增加的树族中选择的sizen随机树中的nodej和noden之间的数量距离。对于那些可以通过树的演化过程来构造的增加的树族的子类，我们给出概率分布，期望和方差的封闭式。此外，对于任意标记1≤j

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