Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice

作者：Chang Shu Chiuan^*; Chen Lung Chi

来源：Journal of Statistical Physics, 2014, 155(3): 500-522.

DOI：10.1007/s10955-014-0961-7

• Domany-Kinzel model
• Directed percolation
• Random walk
• Asymptotic behavior
• Berry-Esseen theorem
• Large deviation

We consider a version of directed bond percolation on the triangular lattice such that vertical edges are directed upward with probability , diagonal edges are directed from lower-left to upper-right or lower-right to upper-left with probability , and horizontal edges are directed rightward with probabilities and one in alternate rows. Let be the probability that there is at least one connected-directed path of occupied edges from to . For each , , but and aspect ratio fixed for the triangular lattice with diagonal edges from lower-left to upper-right, we show that there is an such that as , is , and for , and , respectively. A corresponding result is obtained for the triangular lattice with diagonal edges from lower-right to upper-left. We also investigate the rate of convergence of and the asymptotic behavior of and where and as N up arrow infinity.

• 出版日期2014-5