DISTANCES IN RANDOM PLANE-ORIENTED RECURSIVE TREES

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:41

Article

MAHMOUD, HM

关键词: RECURSIVE TREE;    DEPTH;    PATH LENGTH;    LIMIT THEOREM;    MARTINGALE;   

DOI  :  10.1016/0377-0427(92)90252-S

来源: Elsevier

【 摘 要 】

The average number of nodes in a stratum of random plane-oriented recursive trees is found. The expression is used to determine the exact probability distribution of the depth of the nth node. It is further shown that the limiting distribution of the normalized depth of this node is the standard normal distribution. Via martingales, the normalized external path length is shown to converge almost surely and in L2 to a limiting random variable.

【 授权许可】

Free