Graduate Thesis Or Dissertation

 

Some tree structure function asymptotics 公开 Deposited

可下载的内容

下载PDF文件
https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/3n2043725

Descriptions

Attribute NameValues
Creator
Abstract
  • We consider some mathematical problems involving the asymptotic analysis of rooted tree structures. River channel networks, patterns of electric discharge, eletrochemical deposition and botanical trees themselves are examples of such naturally occuring structures. In this thesis we will study the width function aymptotics of some random trees as well as certain deterministic self-similar trees. The width function counts the number of branches as a function of the distance to the root. The main results are: (i) A proof of convergence of the width function to a Brownian excursion local time process; (ii) A probabilistic derivation of the expected width function asymptotic; (iii) Asymptotic computation of width functions for a class of deterministic self-similar trees. The result (i) solves a weak version of a conjecture of Aldous (1991) in the case of geometrically distributed offspring and corrects a scale factor there. This result provides the basis for the approach in (ii). The results in (iii) apply to the expected Galton-Watson branching tree under appropriate conditioning.
Resource Type
Date Available
Date Issued
Degree Level
Degree Name
Degree Field
Degree Grantor
Commencement Year
Advisor
Academic Affiliation
Non-Academic Affiliation
Subject
权利声明
Publisher
Peer Reviewed
Language
Digitization Specifications
  • Master files scanned at 600 ppi (256 Grayscale) using Capture Perfect 3.0.82 on a Canon DR-9080C in TIF format. PDF derivative scanned at 300 ppi (256 B&W), using Capture Perfect 3.0.82, on a Canon DR-9080C. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
Replaces

关联

Parents:

This work has no parents.

属于 Collection:

单件