Limit distribution for the maximum degree of a random recursive tree
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摘要
If a recursive tree is selected uniformly at random from among all recursive trees on n vertices, then the distribution of the maximum in-degree Δ is given asymptotically by the following theorem: for any fixed integer d,Pn(Δ⩽⌊μn⌋+d)=exp(−2{μn}−d−1)+o(1)as n→∞, where μn=log2n. (As usual, ⌊μn⌋ denotes the greatest integer less than or equal to μn, and {μn}=μn−⌊μn⌋.) The proof makes extensive use of asymptotic approximations for the partial sums of the exponential series.
论文关键词:Asymptotic enumeration,Degree,Recursive,Szegő,Exponential series,Tree
论文评审过程:Received 2 April 2001, Revised 25 April 2001, Available online 9 April 2002.
论文官网地址:https://doi.org/10.1016/S0377-0427(01)00460-5