随机递归树模型中两个基于距离的索引的极限律

IF 0.3 Q4 COMPUTER SCIENCE, THEORY & METHODS

Acta Universitatis Sapientiae Informatica Pub Date : 2022-08-01 DOI:10.2478/ausi-2022-0003

S. Naderi, R. Kazemi, M. Behzadi

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引用次数: 0

摘要

摘要本文给出了两类随机递归树的总路径长度和Sackin索引的几个结果。在随机递归树中，用收缩方法给出了归一化的Sackin指数的极限分布。此外，我们还证明了归一化总路径长度收敛于L2，并且几乎肯定地收敛于平面递归树中通过鞅的极限随机变量。

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Limit laws for two distance-based indices in random recursive tree models

Abstract In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the normalized version of the Sackin index is given by the contraction method in random recursive trees. Also, we show the normalized total path length converges in L2 and almost surely to a limiting random variable in plane-oriented recursive trees via martingales.

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Acta Universitatis Sapientiae Informatica COMPUTER SCIENCE, THEORY & METHODS-

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