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Tree limits and limits of random trees

Part of: Markov processes Combinatorial probability Graph theory

Published online by Cambridge University Press:  31 March 2021

Svante Janson
Svante Janson*
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06Uppsala, Sweden
*
Email: [email protected]
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Abstract

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We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton–Watson trees and simply generated trees, for split trees and generalized split trees (as defined here), and for trees defined by a continuous-time branching process. These general results include, for example, random labelled trees, ordered trees, random recursive trees, preferential attachment trees, and binary search trees.

MSC classification

Primary: 60C05: Combinatorial probability 05C05: Trees
Secondary: 05C12: Distance in graphs 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 6 , November 2021 , pp. 849 - 893
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

†

Supported by the Knut and AliceWallenberg Foundation

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