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Small trees in supercritical random forests

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  29 September 2020

Tao Lei
Tao Lei*
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montréal, QCH3A 0B9, Canada URL: http://www.math.mcgill.ca/~tlei/
*
e-mail: tao.lei@mail.mcgill.ca
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Abstract

We study the scaling limit of a random forest with prescribed degree sequence in the regime that the largest tree consists of all but a vanishing fraction of nodes. We give a description of the limit of the forest consisting of the small trees, by relating a plane forest to a marked cyclic forest and its corresponding skip-free walk.

Keywords

Random forestscontinuum random treesdegree sequenceGHP convergence

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C05: Trees 05C80: Random graphs
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 3 , September 2021 , pp. 605 - 623
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Copyright
© Canadian Mathematical Society 2020

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