Cutting down trees with a Markov chainsaw

Abstract : 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, non-asymptotic 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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Contributor : Nicolas Broutin <>
Submitted on : Sunday, January 13, 2013 - 4:04:19 PM
Last modification on : Monday, February 18, 2019 - 7:52:04 PM

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Louigi Addario-Berry, Nicolas Broutin, Cecilia Holmgren. Cutting down trees with a Markov chainsaw. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2014, 24 (6), pp.2297-2339. ⟨10.1214/13-AAP978⟩. ⟨hal-00773364⟩

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