### Abstract

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 .

Original language | English |
---|---|

Article number | 023212 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2017 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2017 Feb 27 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2017*(2), [023212]. https://doi.org/10.1088/1742-5468/2017/2/023212

}

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2017, no. 2, 023212. https://doi.org/10.1088/1742-5468/2017/2/023212

**Asymptotic behavior for a generalized Domany-Kinzel model.** / Chang, Shu-Chiuan; Chen, Lung Chi; Huang, Chien Hao.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic behavior for a generalized Domany-Kinzel model

AU - Chang, Shu-Chiuan

AU - Chen, Lung Chi

AU - Huang, Chien Hao

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

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 -