随机试验中距离的振荡分布
The oscillatory distribution of distances in random tries
摘要：
本文研究了随机trie树中n个关键字之间的距离Δ n。分析技术，如梅林变换和泊松化和去泊松化之间的偏移，捕捉这些随机距离的平均值和方差的小波动。平均值随着键的数量而递增，但奇怪的是方差仍然是O（1），因为n \to \infty。证明了中心随机变量Δ n^*=Δ n- \lfloor 2 \log_2 n \rfloor不具有极限分布，而是在两个分布之间振荡.
英文摘要：
We investigate Δ_n, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O(1), as n\to\infty. It is demonstrated that the centered random variable Δ_n^*=Δ_n-\lfloor2\log_2n\rfloor does not have a limit distribution, but rather oscillates between two distributions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
