AUTHOR=Sun Yu , Liu Xiaobei , Li Xiaoyan 

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

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1076276

DOI=10.3389/fphy.2022.1076276

ISSN=2296-424X

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