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2015 Random recursive trees: a boundary theory approach
Rudolf Grübel, Igor Michailow
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Electron. J. Probab. 20: 1-22 (2015). DOI: 10.1214/EJP.v20-3832


We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in terms of the input sequence of the algorithm. We further show that this approach can be used to obtain strong limit theorems for various tree functionals, such as path length or the Wiener index.


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Rudolf Grübel. Igor Michailow. "Random recursive trees: a boundary theory approach." Electron. J. Probab. 20 1 - 22, 2015.


Accepted: 1 April 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1327.60031
MathSciNet: MR3335828
Digital Object Identifier: 10.1214/EJP.v20-3832

Primary: 60C05
Secondary: 05C05 , 60J50 , 68Q87

Keywords: Doob-Martin compactification , Harris trees , Markov chains , path length , Random trees , Wiener index

Vol.20 • 2015
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