Determining entire mean first-passage time for Cayley networks

Xiaoqian Wang (), Meifeng Dai, Yufei Chen (), Yue Zong (), Yu Sun () and Weiyi Su ()
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Xiaoqian Wang: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Meifeng Dai: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Yufei Chen: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Yue Zong: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Yu Sun: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Weiyi Su: #x2020;Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 01, 1-10

Abstract: In this paper, we consider the entire mean first-passage time (EMFPT) with random walks for Cayley networks. We use Laplacian spectra to calculate the EMFPT. Firstly, we calculate the constant term and monomial coefficient of characteristic polynomial. By using the Vieta theorem, we then obtain the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix. Finally, we obtain the scaling of the EMFPT for Cayley networks by using the relationship between the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix and the EMFPT. We expect that our method can be adapted to other types of self-similar networks, such as vicsek networks, polymer networks.

Keywords: Entire mean first-passage time; Laplacian spectra; Cayley networks; Vieta theorem (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0129183118500092

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