Bandwidths and profiles of trees
Journal of Combinatorial Theory Series B
On the profile of random trees
Random Structures & Algorithms
Convergence of branching processes to the local time of a Bessel process
proceedings of the eighth international conference on Random structures and algorithms
Average Profile of the Generalized Digital Search Tree and the Generalized Lempel--Ziv Algorithm
SIAM Journal on Computing
On the covariance of the level sizes in random recursive trees
Random Structures & Algorithms
On Robson's convergence and boundedness conjectures concerning the height of binary search trees
Theoretical Computer Science
Bimodality and Phase Transitions in the Profile Variance of Random Binary Search Trees
SIAM Journal on Discrete Mathematics
Nodes of large degree in random trees and forests
Random Structures & Algorithms
Profiles of random trees: Plane-oriented recursive trees
Random Structures & Algorithms
The distribution of nodes of given degree in random trees
Journal of Graph Theory
Analytic Combinatorics
Random Trees: An Interplay between Combinatorics and Probability
Random Trees: An Interplay between Combinatorics and Probability
The degree profile of random Pólya trees
Journal of Combinatorial Theory Series A
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We consider the number of nodes in the levels of unlabelled rooted random trees and show that the stochastic process given by the properly scaled level sizes weakly converges to the local time of a standard Brownian excursion. Furthermore we compute the average and the distribution of the height of such trees. These results extend existing results for conditioned Galton-Watson trees and forests to the case of unlabelled rooted trees and show that they behave in this respect essentially like a conditioned Galton-Watson process.