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Inhomogeneous Site Percolation on an Irregular Bethe Lattice with Random Site Distribution

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Abstract

In this paper, we study inhomogeneous site percolation on an irregular Bethe lattice, for considering that percolation often occurs on irregular grids or lattices with variable site neighbours in real-world problems. The explicit expression for cluster-size distribution of this percolation is derived based on probability theory. Moreover, the exact formulas for critical occupation probability, mean cluster size, and percolation probability are obtained using generating function method and generalised recursive approach. In addition, sensitivity analysis and numerical simulation are given to deepen and illustrate the results.

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Acknowledgements

This work is supported by Grants from the Natural Science Foundation of China (Grant No. 11271339), the Plan for Scientific Innovation Talent of Henan Province (164200510011), Innovative Research Team of Science and Technology in Henan Province (17IRTSTHN007), and Opening fund of State Key Laboratory of Nonlinear Mechanics.

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  1. School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, People’s Republic of China

    Jingli Ren & Liying Zhang

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  1. Jingli Ren
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  2. Liying Zhang
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Correspondence to Jingli Ren.

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Ren, J., Zhang, L. Inhomogeneous Site Percolation on an Irregular Bethe Lattice with Random Site Distribution. J Stat Phys 168, 394–407 (2017). https://doi.org/10.1007/s10955-017-1803-1

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