Asymptotic behavior for a version of directed percolation on the honeycomb lattice

Shu-Chiuan Chang and Lung-Chi Chen

Physica A: Statistical Mechanics and its Applications, 2015, vol. 436, issue C, 547-557

Abstract: We consider a version of directed bond percolation on the honeycomb lattice as a brick lattice such that vertical edges are directed upward with probability y, and horizontal edges are directed rightward with probabilities x and one in alternate rows. Let τ(M,N) be the probability that there is at least one connected-directed path of occupied edges from (0,0) to (M,N). For each x∈(0,1], y∈(0,1] and aspect ratio α=M/N fixed, we show that there is a critical value αc=(1−x+xy)(1+x−xy)/(xy2) such that as N→∞, τ(M,N) is 1, 0 and 1/2 for α>αc, α<αc and α=αc, respectively. We also investigate the rate of convergence of τ(M,N) and the asymptotic behavior of τ(MN−,N) and τ(MN+,N) where MN−/N↑αc and MN+/N↓αc as N↑∞.

Keywords: Domany–Kinzel model; Directed percolation; Random walk; Asymptotic behavior; Berry–Esseen theorem; Large deviation (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:436:y:2015:i:c:p:547-557

DOI: 10.1016/j.physa.2015.05.083

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