Multifractal spectra provide a way of encapsulating information about the nature of random measures living on the boundary of a Galton-Watson tree. In this thesis we investigate the ;tal spectrum for various harmonic measures. These are the hitting distributions of various random walks on the Galton-Watson tree. We use martingales and change of measure techniques for calculating Hausdorff dimension to establish the spectra. We also investigate a multifractal spectrum for the interaction between visibility measure and the branching measure.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:500714 |
| Date | January 2009 |
| Creators | Kinnison, Adam Lester |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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