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

¹ School of Computer Science, Fudan University - Shanghai 200433, China
² Shanghai Key Lab of Intelligent Information Processing, Fudan University - Shanghai 200433, China
³ Department of Electronic Engineering, City University of Hong Kong - Hong Kong SAR, China

^a zhangzz@fudan.edu.cn
^b eegchen@cityu.edu.hk

Received: 23 August 2011
Accepted: 23 September 2011

Abstract

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.