Hitting time for random walks on the Sierpinski network and the half Sierpinski network

Abstract

We consider the unbiased random walk on the Sierpinski network (Sn◦N) and the half Sierpinski network (HSn◦N), where n is the generation. Different from the existing works on the Sierpinski gasket, Sn◦N is generated by the nested method and HSn◦N is half of Sn◦N based on the vertical cutting of the symmetry axis. We study the hitting time on Sn◦N and HSn◦N. According to the complete symmetry and structural properties of Sn◦N, we derive the exact expressions of the hitting time on the nth generation of Sn◦N and HSn◦N. The curves of the hitting time for the two networks are almost consistent when n is large enough. The result indicates that the diffusion efficiency of HSn◦N has not changed greatly compared with Sn◦N at a large scale.