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Automorphisms of Random Trees

Authors Christoffer Olsson , Stephan Wagner



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Author Details

Christoffer Olsson
  • Department of Mathematics, Uppsala University, Sweden
Stephan Wagner
  • Department of Mathematics, Uppsala University, Sweden

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Christoffer Olsson and Stephan Wagner. Automorphisms of Random Trees. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 16:1-16:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.AofA.2022.16

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Random graphs
  • Mathematics of computing → Generating functions
Keywords
  • random tree
  • Galton-Watson tree
  • Pólya tree
  • automorphism group
  • central limit theorem

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References

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