Dissertation/Thesis Abstract

Phase Transitions on Static and Evolving Networks: Effects of Competition, Zealotry, and Growth
by Waagen, Alex, Ph.D., University of California, Davis, 2014, 156; 3685308
Abstract (Summary)

This thesis consists of studies of network processes with an emphasis on phase transitions. Various network models are studied and phase transitions are categorized as discontinuous, smooth, or continuous but non-differentiable. In one case we define a simple degree-based network model which exhibits a truly discontinuous phase transition to large-scale continuity, and prove this result rigorously. We also show that an altered version of the naming game exhibits critical points which appear to follow an exact log-normal curve. Additionally, we define a model which introduced edge competition to percolation on a growing network and a model which replicates features observed in weekly activity graphs from Facebook gifting applications. The goal is to determine which mechanisms lead to different categories of phase transitions and delay or enhance the onset of the phase transition. A second goal is to introduce growth and evolution into network models, in order to define models which better replicate features of real-world networks.

Indexing (document details)
Advisor: D'Souza, Raissa M.
Commitee: Crutchfield, Jampes P., Gravner, Janko
School: University of California, Davis
Department: Applied Mathematics
School Location: United States -- California
Source: DAI-B 76/08(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics, Statistics
Keywords: Achlioptas process, Networks, Opinion dynamics, Phase transition, Statistical physics
Publication Number: 3685308
ISBN: 9781321610185
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