Eigenvalue spectrum of transition matrix of dual Sierpinski gaskets and its applications

The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embed...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-08, Vol.45 (34), p.345101-1-345101-11
Main Authors: Wu, Shunqi, Zhang, Zhongzhi
Format: Article
Language:English
Subjects:
Eigenvalues
Exact sciences and technology
Fractal analysis
Fractals
Gaskets
Graph theory
Mathematical analysis
Networks
Physics
Random walk
Spectra
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Summary:The eigenvalue spectrum of the transition matrix of a network contains much information about its structural properties and is related to the behavior of various dynamical processes performed on it. In this paper, we study the eigenvalues of the transition matrix of the dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We obtain all the eigenvalues, as well as their corresponding degeneracies, by making use of the spectral decimation technique. We then apply the obtained eigenvalues to determine the exact number of spanning trees in the studied fractals and derive an explicit formula of the eigentime identity for random walks taking place on them.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/34/345101