On the peel number and the leaf-height of Galton–Watson trees

  title={On the peel number and the leaf-height of Galton–Watson trees},
  author={Luc Devroye and Marcel K. Goh and Rosie Y. Zhao},
  journal={Combinatorics, Probability and Computing},
<jats:p>We study several parameters of a random Bienaymé–Galton–Watson tree <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0963548322000128_inline1.png" /> <jats:tex-math> $T_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of size <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png… 

Figures and Tables from this paper



Formal power series and the total progeny in a branching process

Analysis of three graph parameters for random trees

It is shown that for simply generated tree families that the mean and the variance of each of the three parameters under consideration behave for a randomly chosen tree of size n asymptotically ∼μn and ∼νn, where the constants μ and ν depend on the tree family and the parameter studied.

Asymptotic Fringe Distributions for General Families of Random Trees

The total progeny in a branching process and a related random walk

This paper is a continuation of [1]. The techniques of [1] are used to get specific information about the distribution of the total progeny in a branching process. This distribution is also related

An Estimate for Concentration Functions

Let $\xi _1 , \cdots ,\xi _n $ be independent random variables, \[ Q_k \{ l \} = \mathop {\sup }\limits_x {\bf P} \{ {x \leqq \xi _k \leqq x + l} \}, \]\[ Q \{ L \} = \mathop {\sup }\limits_x {\bf P}

Protection numbers in simply generated trees and Pólya trees

We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P?lya trees, and in unlabelled non-plane binary trees, when the

Subdiffusive behavior of random walk on a random cluster

On considere deux cas de marche aleatoire {X n } n≥0 sur un graphe aleatoire #7B-G. Dans le cas ou #7B-G est l'arbre d'un processus de branchement critique, conditionne par la non-extinction, si h(x)

Recursive functions on conditional Galton‐Watson trees

The limit behavior when the leaf values are drawn independently from a fixed distribution on $S$ is described, and the tree $T_n$ is a random Galton--Watson tree of size n.