2011/10/31 by Louigi Addario-Berry, Louigi Addario‐Berry, Nicolas Broutin +1 · 36 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Biology #Brownian excursion #Brownian motion #Combinatorics #Computer science #Discrete mathematics #Distribution (mathematics) #Markov Chains and Monte Carlo Methods #Markov chain #Mathematical analysis #Mathematical proof #Mathematics #Physics #Poisson distribution #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Transformation (genetics) #Tree (set theory) #math.CO #math.PR
paper · pdf · doi:10.1214/13-aap978
published in The Annals of Applied Probability 24(6) (Institute of Mathematical Statistics) · 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)
openalex publication_date 2014/08/26 · arxiv created 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.