Asymptotic behavior for a generalized Domany-Kinzel model

Shu-Chiuan Chang, Lung Chi Chen, Chien Hao Huang

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Article number023212
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2017
Issue number2
DOIs
Publication statusPublished - 2017 Feb 27

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Asymptotic Behavior
Square Lattice
Honeycomb
Critical value
Vertical
Model
bricks
Aspect Ratio
aspect ratio
Rate of Convergence
Horizontal
Odd
Asymptotic behavior
Path

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, No. 2, 023212, 27.02.2017.

Research output: Contribution to journalArticle

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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 .

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