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arXiv · 1110.6455

Cutting down trees with a Markov chainsaw

Louigi Addario-Berry·Nicolas Broutin·Cecilia Holmgren
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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, 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. 2014-09-05. Cutting down trees with a Markov chainsaw. https://doi.org/10.1214/13-aap978

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