Complete spectrum of the stochastic master equation for random walks on treelike fractals

We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues being provided through an explicit recursive relation. We also...

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Bibliographic Details
Published in:Europhysics letters 2011-11, Vol.96 (4), p.40009
Main Authors: Zhang, Zhongzhi, Wu, Bin, Chen, Guanrong
Format: Article
Language:English
Subjects:
05.40.Fb
05.45.Df
05.60.Cd
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Summary:We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues being provided through an explicit recursive relation. We also evaluate the smallest eigenvalue and show that its reciprocal is approximately equal to the mean trapping time. We expect that our technique can also be adapted to other regular fractals with treelike structures.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/96/40009