Geodesic
The profile of unlabeled trees
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005).

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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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     author = {Gittenberger, Bernhard},
     title = {The profile of unlabeled trees},
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Gittenberger, Bernhard. The profile of unlabeled trees. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005). doi : 10.46298/dmtcs.3352. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3352/

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