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Explicit Determination of Mean First-passage Time for Random Walks on Deterministic Uniform Recursive Trees by Zhang, Zhongzhi; Qi, Yi; Zhou, Shuigeng; Gao, Shuyang; Guan, Jihong is a scholarly article available to read on EtoBox.

What is Explicit Determination of Mean First-passage Time for Random Walks on Deterministic Uniform Recursive Trees about?

The determination of mean first-passage time (MFPT) for random walks in networks is a theoretical challenge, and is a topic of considerable recent interest within the physics community. In this paper, according to the known connections between MFPT, effective resistance, and the eigenvalues of graph Laplacian, we first study analytically the MFPT between all node pairs of a class of growing treelike networks, which we term deterministic uniform recursive trees (DURTs), since one of its particular cases is a deterministic version of the famous uniform recursive tree. The interesting quantity is determined exactly through the recursive relation of the Laplacian spectra obtained from the special construction of DURTs. The analytical result shows that the MFPT between all couples of nodes in DURTs varies as $N \ln N$ for large networks with node number $N$. Second, we study trapping on a particular network of DURTs, focusing on a special case with the immobile trap positioned at a node having largest degree. We determine exactly the average trapping time (ATT) that is defined as the average of FPT from all nodes to the trap. In contrast to the scaling of the MFPT, the leading behavior

Author

Zhang, Zhongzhi; Qi, Yi; Zhou, Shuigeng; Gao, Shuyang; Guan, Jihong

Published

2009

Language

EN