Return to search

Boundary theory of random walk and fractal analysis.

Wong, Ting Kam Leonard. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 91-97) and index. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Problems of fractal analysis --- p.6 / Chapter 1.2 --- The boundary theory approach --- p.7 / Chapter 1.3 --- Summary of the thesis --- p.9 / Chapter 2 --- Martin boundary --- p.13 / Chapter 2.1 --- Markov chains and discrete potential theory --- p.13 / Chapter 2.2 --- Martin compactification --- p.18 / Chapter 2.3 --- Convergence to boundary and integral representations --- p.20 / Chapter 2.4 --- Dirichlet problem at infinity --- p.25 / Chapter 3 --- Hyperbolic boundary --- p.27 / Chapter 3.1 --- Random walks on infinite graphs --- p.27 / Chapter 3.2 --- Hyperbolic compactification --- p.31 / Chapter 3.3 --- Ancona's theorem --- p.33 / Chapter 3.4 --- Self-similar sets as hyperbolic boundaries --- p.34 / Chapter 3.5 --- Hyperbolic compactification of augmented rooted trees --- p.44 / Chapter 4 --- Simple random walk on Sierpinski graphs --- p.47 / Chapter 4.1 --- Hcuristic argument for d = 1 --- p.48 / Chapter 4.2 --- Symmetries and group invariance --- p.51 / Chapter 4.3 --- Reflection principle --- p.54 / Chapter 4.4 --- Self-similar identity and hitting distribution --- p.60 / Chapter 4.5 --- Remarks and Open Questions --- p.64 / Chapter 5 --- Induced Dirichlet forms on self-similar sets --- p.66 / Chapter 5.1 --- Basics of Dirichlet forms --- p.67 / Chapter 5.2 --- Motivation: the classical Douglas integral --- p.68 / Chapter 5.3 --- Graph energy and the induced forms --- p.69 / Chapter 5.4 --- Induced Dirichlet forms on self-similar sets --- p.74 / Chapter 5.5 --- A uniform tail estimate via coupling --- p.83 / Chapter 5.6 --- Remarks and open questions --- p.89 / Index of selected terms --- p.98

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327065
Date January 2011
ContributorsWong, Ting Kam Leonard., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 99 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Page generated in 0.0019 seconds