TY - JOUR

T1 - Asymptotic behavior for a generalized Domany-Kinzel model

AU - Chang, Shu Chiuan

AU - Chen, Lung Chi

AU - Huang, Chien Hao

N1 - Funding Information:
The research of SCC was partially supported by Ministry of Science and Technology grants MOST 103-2918-I-006-016 and MOST 105-2112-M-006-007. The research of LCC was partially supported by the mathematics division of the National Center for Theoretical Sciences (NCTS) and the Ministry of Science and Technology grant MOST 104-2115-M-004-003-MY3. The research of CHH was partially supported by the postdoctoral fellowship granted by Institute of Mathematics, Academia Sinica.

PY - 2017/2/27

Y1 - 2017/2/27

N2 - We consider a version of directed bond percolation on the square lattice such that horizontal edges are directed rightward with probabilities one, and vertical edges are directed upward with probabilities p 1, p 2 alternatively in even rows and probabilities p 2, p 1 alternatively in odd rows, where , , but . Let be the probability that there is at least one connected-directed path of occupied edges from (0, 0) to (M,N). Defining the aspect ratio , we show that there is a critical value such that as , is 1, 0 and 1/2 for , and , respectively. In particular, the model reduces to the square lattice with uniform vertical probability when [1], and the model reduces to the honeycomb lattice when one of p 1 and p 2 is equal to 0. We study how the critical value changes between the square lattice and the honeycomb lattice as bricks. In this article, we investigate the rate of convergence of and the asymptotic behavior of and , where and as .

AB - We consider a version of directed bond percolation on the square lattice such that horizontal edges are directed rightward with probabilities one, and vertical edges are directed upward with probabilities p 1, p 2 alternatively in even rows and probabilities p 2, p 1 alternatively in odd rows, where , , but . Let be the probability that there is at least one connected-directed path of occupied edges from (0, 0) to (M,N). Defining the aspect ratio , we show that there is a critical value such that as , is 1, 0 and 1/2 for , and , respectively. In particular, the model reduces to the square lattice with uniform vertical probability when [1], and the model reduces to the honeycomb lattice when one of p 1 and p 2 is equal to 0. We study how the critical value changes between the square lattice and the honeycomb lattice as bricks. In this article, we investigate the rate of convergence of and the asymptotic behavior of and , where and as .

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U2 - 10.1088/1742-5468/2017/2/023212

DO - 10.1088/1742-5468/2017/2/023212

M3 - Article

AN - SCOPUS:85016049352

VL - 2017

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 2

M1 - 023212

ER -