Cutting down trees with a Markov chainsaw
Probability
2014-09-08 v3 Combinatorics
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 . 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.
Keywords
Cite
@article{arxiv.1110.6455,
title = {Cutting down trees with a Markov chainsaw},
author = {Louigi Addario-Berry and Nicolas Broutin and Cecilia Holmgren},
journal= {arXiv preprint arXiv:1110.6455},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AAP978 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)