Abstract
Hierarchical structures have been found in actual complex
systems. Certain hierarchical networks, with a self-similar
structure, exhibit novel properties in a broader spectrum of
dynamics such as synchronization, quantum walks and the epidemic
process, which we explore in this thesis by applying analytical and
numerical methods. We study the structural and spectral properties
of large scale networks, as well as various phenomena on them with
the Renormalization Group (RG) approach. In particular, by applying
RG, we explore the Laplacian spectrum, whichis related to
asymptotic structural features of networks, ranging from the number
of spanning trees to synchronizability. The spectralanalysis also
reveals a deep connection between dynamics and the underlying
structure in processes that include quantum walks and the unusual
Griffiths phase on hierarchical networks considered in this thesis.
This thesis highlights effects of spectral properties on dynamical
processes on networks, and indicates the applicability of RG to
various contexts.
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About this Dissertation
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