Some tree structure function asymptotics Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/3n2043725

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  • 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.
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  • 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.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-05-14T19:48:21Z (GMT) No. of bitstreams: 1 ZhangQing1996.pdf: 462160 bytes, checksum: 7c9a5af274500e274bc0305f0f697214 (MD5)
  • description.provenance : Made available in DSpace on 2010-05-14T19:48:21Z (GMT). No. of bitstreams: 1 ZhangQing1996.pdf: 462160 bytes, checksum: 7c9a5af274500e274bc0305f0f697214 (MD5)
  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-05-14T19:46:27Z (GMT) No. of bitstreams: 1 ZhangQing1996.pdf: 462160 bytes, checksum: 7c9a5af274500e274bc0305f0f697214 (MD5)
  • description.provenance : Submitted by Joe Nguyen (jnscanner@gmail.com) on 2010-05-12T21:50:41Z No. of bitstreams: 1 ZhangQing1996.pdf: 462160 bytes, checksum: 7c9a5af274500e274bc0305f0f697214 (MD5)

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