Random recursive trees: a boundary theory approach *
Random recursive trees: a boundary theory approach *
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DOI：
10.1214/ejp.v20-3832
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发表时间：
2014-06
影响因子：
1.4
通讯作者：
Rudolf Grubel;I. Michailow
中科院分区：
文献类型：
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作者：
Rudolf Grubel;I. Michailow
我们证明了递归树序列的算法构造直接证明了随机递归树在相关的Doob-Martin紧化下的收敛，并给出了关于算法输入序列的极限的表示。我们进一步证明了这种方法可以用来得到各种树泛函的强极限定理，如路径长度或Wiener指数。
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in terms of the input sequence of the algorithm. We further show that this approach can be used to obtain strong limit theorems for various tree functionals, such as path length or the Wiener index.