Multivariate normal limit laws for the numbers of fringe subtrees in m-ary search trees and preferential attachment trees

被引：0
|
作者：
Holmgren, Cecilia [1 ]
Janson, Svante [1 ]
Sileikis, Matas [2 ]
机构：
[1] Uppsala Univ, Dept Math, POB 480, S-75106 Uppsala, Sweden
[2] Charles Univ Prague, Fac Math & Phys, Dept Appl Math, Malostranske Nam 25, CR-11800 Prague, Czech Republic
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2017年 / 24卷 / 02期
基金：
瑞典研究理事会;
关键词：
Random trees; Fringe trees; Normal limit laws; Polya urns; m-ary search trees; Preferential attachment trees; Protected nodes; ASYMPTOTIC JOINT NORMALITY; RECURSIVE TREES; THEOREMS; SIZE; NODES; SPACE;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study fringe subtrees of random m-ary search trees and of preferential attachment trees, by putting them in the context of generalised Polya urns. In particular we show that for the random m-ary search trees with m <= 26 and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree T converges to a normal distribution; more generally, we also prove multivariate normal distribution results for random vectors of such numbers for different fringe subtrees. Furthermore, we show that the number of protected nodes in random m-ary search trees for m <= 26 has asymptotically a normal distribution.
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页数：49
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