Analysis of generating functions and probabilities on trees
type: Item
instance of: scholarly article
zbMATH Open document ID: 1003.60021
author: Michael Drmota
publication date: 2002-02-05T00:00:00Z
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 1701853
zbMATH Keywords: families of tree
zbMATH Keywords: asymptotic estimates
zbMATH Keywords: number of rooted trees
zbMATH Keywords: contour process
zbMATH Keywords: Brownian excursion
MaRDI profile type: Publication
title: Analysis of generating functions and probabilities on trees
review text: The author considers simply generated families of tree and employs analytic tools, the saddle point method and singularity analysis, in order to obtain asymptotic estimates for the coefficients of generating functions counting trees with specific parameters. As an application, he proves an asymptotic formula for the number of rooted trees in a simply generated family of size \(n\) with \(l\) leaves such that the \(m\)th leaf has height \(k\). Under suitable conditions the height of the \(m\)th leaf is Maxwell distributed. He also states that the corresponding contour process converges to Brownian excursion.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].
reviewed by: Andreas N. Philippou
description: scientific article; zbMATH DE number 1701853