Open Access
December 2014 Cutting down trees with a Markov chainsaw
Louigi Addario-Berry, Nicolas Broutin, Cecilia Holmgren
Ann. Appl. Probab. 24(6): 2297-2339 (December 2014). DOI: 10.1214/13-AAP978


We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton–Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny $n$. Our proof is based on a coupling which yields a precise, nonasymptotic distributional result for the case of uniformly random rooted labeled trees (or, equivalently, Poisson Galton–Watson trees conditioned on their size). Our approach also provides a new, random reversible transformation between Brownian excursion and Brownian bridge.


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Louigi Addario-Berry. Nicolas Broutin. Cecilia Holmgren. "Cutting down trees with a Markov chainsaw." Ann. Appl. Probab. 24 (6) 2297 - 2339, December 2014.


Published: December 2014
First available in Project Euclid: 26 August 2014

zbMATH: 1352.60009
MathSciNet: MR3262504
Digital Object Identifier: 10.1214/13-AAP978

Primary: 05C05 , 60C05 , 60F17
Secondary: 11Y16

Keywords: Continuum random tree , Cutting down , Galton–Watson tree , Gromov–Hausdorff convergence , real tree

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 2014
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