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We investigate \Delta_n, the distance between randomly selected pairs ofnodes among n keys in a random trie, which is a kind of digital tree.Analytical techniques, such as the Mellin transform and an excursion betweenpoissonization and depoissonization, capture small fluctuations in the mean andvariance of these random distances. The mean increases logarithmically in thenumber of keys, but curiously enough the variance remains O(1), as n\to\infty.It is demonstrated that the centered random variable\Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit distribution,but rather oscillates between two distributions.

The oscillatory distribution of distances in random tries