中国科学技术大学学报 ›› 2019, Vol. 49 ›› Issue (3): 173-181.DOI: 10.3969/j.issn.0253-2778.2019.03.001
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冯群强
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摘要： 主要讨论了随机平面根树的度分布.对任意 d≥1 ,证明了在含有 n 条边的随机平面根树中,当 n→SymboleB@ 时,度数为 d 的顶点数目在合适的正则化条件下具有渐近正态性,还给出了该数目期望和方差的渐近表达式.在证明过程中主要使用了一种解析的方法.
关键词: 随机树, 度分布, 鞍点法, Hurwitz定理
Abstract: The degree profile in a random planted plane tree was considered. For any d≥1 , it was proven that under suitable normalization, the number of vertices of degree d in a random planted plane tree with n edges has asymptotic normality, as n goes to infinity. The asymptotic formulae for the expectation and variance of this random variable were also given. An analytical method was employed in the proof.
Key words: random tree, degree profile, saddle point method, Hurwitz theorem
冯群强，郑伯泽. 一种随机树度分布的解析方法[J]. 中国科学技术大学学报, 2019, 49(3): 173-181.
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链接本文: http://just-cn.ustc.edu.cn/CN/10.3969/j.issn.0253-2778.2019.03.001
http://just-cn.ustc.edu.cn/CN/Y2019/V49/I3/173
