The degree profile of random Polya trees

被引：0
|
作者：
Gittenberger, Bernhard [1 ]
Kraus, Veronika [2 ]
机构：
[1] TU Wien, Inst Discrete Math & Geometry, A-1040 Vienna, Austria
[2] UMIT, Inst Bioinformat & Translat Res, A-6020 Hall In Tirol, Austria
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2012年 / 119卷 / 07期
关键词：
Unlabelled trees; Profile; Nodes of fixed degree; Brownian excursion; Local time; BINARY SEARCH-TREES; RANDOM RECURSIVE TREES; FUNCTIONAL LIMIT-THEOREM; CONTINUUM RANDOM TREE; LARGE PLANAR MAPS; BROWNIAN EXCURSION; LOCAL TIME; DENSITY; FORESTS; HEIGHT;
D O I：
10.1016/j.jcta.2012.04.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the profile of random Polya trees of size n when only nodes of degree d are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process converges weakly to a Brownian excursion local time. Moreover, we investigate the joint distribution of the number of nodes of degrees d(1) and d(2) on the same level of the tree. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：1528 / 1557
页数：30
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