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政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/80556

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/80556

Title:	Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice
Authors:	陳隆奇 Chen, Lung-Chi Chang, Shu-Chiuan
Contributors:	應數系
Keywords:	Domany–Kinzel;model;Directed percolation;Random walk;Asymptotic behavior;Berry–Esseen theorem;Large deviation
Date:	2014-05
Issue Date:	2016-01-13 16:23:26 (UTC+8)
Abstract:	We consider a version of directed bond percolation on the triangular lattice such that vertical edges are directed upward with probability y, diagonal edges are directed from lower-left to upper-right or lower-right to upper-left with probability d, 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), d∈[0,1) but (1−y)(1−d)≠1 and aspect ratio α=M/N fixed for the triangular lattice with diagonal edges from lower-left to upper-right, we show that there is an αc=(d−y−dy)/[2(d+y−dy)]+[1−(1−d)2(1−y)2x]/[2(d+y−dy)2] such that as N→∞, τ(M,N) is 1, 0 and 1/2 for α>αc, α<αc and α=αc, 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 τ(M,N) and the asymptotic behavior of τ(M−N,N) and τ(M+N,N) where M−N/N↑αc and M+N/N↓αc as N↑∞.
Relation:	Journal of Statistical Physics, 155(3), 500-522
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1007/s10955-014-0961-7
DOI:	10.1007/s10955-014-0961-7
Appears in Collections:	[應用數學系] 期刊論文

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