中文摘要：

摘要：用泊松变换的方法研究了由二叉分裂算法所产生的随机树上的随机路径的长度，首次得到了关于其数学期望的确切表达式．在此基础上；对该期望的渐近性状进行了分析，证明了＂-3被分裂的集合的大小咒趋于无穷时，随机路径长度的期望具有logz咒的阶．

英文摘要：

The length of the random path generated by the Bernoulli splitting algorithm was studied by means of Poisson transformation. For the first time the exact expression of this expectation was obtained. Based on this expression, the asymptotic analysis of the expectation of the random path were presented. Thus it was proved that as the set size n goes to＇infinite,the expectation of the random path length has the order of log2n.