Cutting down trees with a Markov chainsaw

Details Cutting down trees with a Markov chainsaw Cutting down trees with a Markov chainsaw

2011-10-28

arxiv.org/abs/1110.6455v1

Mathematics

Probability

23 pages, 1 figure

Scientific paper

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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