The Annals of Applied Probability

Cutting down trees with a Markov chainsaw

Louigi Addario-Berry, Nicolas Broutin, and Cecilia Holmgren

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 6 (2014), 2297-2339.

Dates
First available in Project Euclid: 26 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1409058033

Digital Object Identifier
doi:10.1214/13-AAP978

Mathematical Reviews number (MathSciNet)
MR3262504

Zentralblatt MATH identifier
1352.60009

Subjects
Primary: 60C05: Combinatorial probability 60F17: Functional limit theorems; invariance principles 05C05: Trees
Secondary: 11Y16: Algorithms; complexity [See also 68Q25]

Keywords
Cutting down Galton–Watson tree real tree continuum random tree Gromov–Hausdorff convergence

Citation

Addario-Berry, Louigi; Broutin, Nicolas; Holmgren, Cecilia. Cutting down trees with a Markov chainsaw. Ann. Appl. Probab. 24 (2014), no. 6, 2297--2339. doi:10.1214/13-AAP978. https://projecteuclid.org/euclid.aoap/1409058033


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