| author: | Bernhard Gittenberger |
|---|---|
| title: | The profile of unlabeled trees |
| keywords: | unlabeled trees, profile, Brownian excursion, local time |
| abstract: |
We consider the number of nodes in the levels of unlabeled
rooted random trees and show that the joint distribution of
several level sizes (where the level number is scaled by
√
) weakly converges to the distribution of the local
time of a Brownian excursion evaluated at the times
corresponding to the level numbers. This extends existing
results for simply generated trees and forests to the case
of unlabeled rooted trees.
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| reference: | Bernhard Gittenberger (2005), The profile of unlabeled trees, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 167-172 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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