A central limit theorem for additive functionals of increasing trees
A central limit theorem for additive functionals of increasing trees
复制标题
增树泛函的中心极限定理
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
S. Wagner
中科院分区：
文献类型：
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作者：
D. Ralaivaosaona;S. Wagner
摘要 如果树函数满足 $F(T) = \sum_{j=1}^k F(B_j) + f(T)$ 形式的递归，则称为加性函数，其中 B1, …, Bk 是树 T 的分支，f (T) 是收费函数。我们在收费函数的适当假设下证明了 d 元增树的加性泛函的一般中心极限定理。同样的方法也适用于广义平面递增树（GPORT）。我们的主要应用之一是对数正态律，我们证明了 d 元递增树的自同构群的大小，但也涵盖了其他示例（旧的和新的）。
Abstract A tree functional is called additive if it satisfies a recursion of the form $F(T) = \sum_{j=1}^k F(B_j) + f(T)$, where B1, …, Bk are the branches of the tree T and f (T) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the toll function. The same method also applies to generalized plane-oriented increasing trees (GPORTs). One of our main applications is a log-normal law that we prove for the size of the automorphism group of d-ary increasing trees, but other examples (old and new) are covered as well.