Sciweavers

RSA
2002

On the covariance of the level sizes in random recursive trees

13 years 5 months ago
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.
Remco van der Hofstad, Gerard Hooghiemstra, Piet V
Added 23 Dec 2010
Updated 23 Dec 2010
Type Journal
Year 2002
Where RSA
Authors Remco van der Hofstad, Gerard Hooghiemstra, Piet Van Mieghem
Comments (0)