On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. Key words and phrases: Recursive trees, covariance of level sizes, convergence in probability, convergence in total variation. AMS 1991 Subject classifications: Primary 05C05, 60C05, Secondary 60F25, 60F99, 05C80.

• Type: Journal
• Year: 2002
• Where: RSA
• Authors: Remco van der Hofstad, Gerard Hooghiemstra, Piet Van Mieghem
• Keywords: Probability Distribution, Random Recursive Trees, Recursive Trees, RSA 2002