Eur. Phys. J. B 82, 91-96 (2011)
https://doi.org/10.1140/epjb/e2011-20338-0

Random walks on dual Sierpinski gaskets

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

Corresponding author: ^a zhangzz@fudan.edu.cn

Received: 21 March 2011
Revised: 5 May 2011
Published online: 21 June 2011

Abstract

We study an unbiased random walk on dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We first determine the mean first-passage time (MFPT) between a particular pair of nodes based on the connection between the MFPTs and the effective resistance. Then, by using the Laplacian spectra, we evaluate analytically the global MFPT (GMFPT), i.e., MFPT between two nodes averaged over all node pairs. Concerning these two quantities, we obtain explicit solutions and show how they vary with the number of network nodes. Finally, we relate our results for the case of d = 2 to the well-known Hanoi Towers problem.