# The profile of unlabeled trees

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 $\sqrt{n}$) 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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Conference papers
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Cited literature [19 references]

https://hal.inria.fr/hal-01184024
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Submitted on : Wednesday, August 12, 2015 - 3:51:16 PM
Last modification on : Wednesday, May 10, 2017 - 5:39:14 PM
Long-term archiving on: : Friday, November 13, 2015 - 11:39:54 AM

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### Identifiers

• HAL Id : hal-01184024, version 1

### Citation

Bernhard Gittenberger. The profile of unlabeled trees. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.167-172. ⟨hal-01184024⟩

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