License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2022.16
URN: urn:nbn:de:0030-drops-161026
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16102/
Olsson, Christoffer ;
Wagner, Stephan
Automorphisms of Random Trees
Abstract
We study the size of the automorphism group of two different types of random trees: Galton-Watson trees and Pólya trees. In both cases, we prove that it asymptotically follows a log-normal distribution. While the proof for Galton-Watson trees mainly relies on probabilistic arguments and a general result on additive tree functionals, generating functions are used in the case of Pólya trees.
BibTeX - Entry
@InProceedings{olsson_et_al:LIPIcs.AofA.2022.16,
author = {Olsson, Christoffer and Wagner, Stephan},
title = {{Automorphisms of Random Trees}},
booktitle = {33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
pages = {16:1--16:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-230-3},
ISSN = {1868-8969},
year = {2022},
volume = {225},
editor = {Ward, Mark Daniel},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16102},
URN = {urn:nbn:de:0030-drops-161026},
doi = {10.4230/LIPIcs.AofA.2022.16},
annote = {Keywords: random tree, Galton-Watson tree, P\'{o}lya tree, automorphism group, central limit theorem}
}
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Keywords: |
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random tree, Galton-Watson tree, Pólya tree, automorphism group, central limit theorem |
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Collection: |
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33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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08.06.2022 |
