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政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/80553

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/80553

Title:	Asymptotic behavior for a version of directed percolation on the honeycomb lattice
Authors:	張書銓;陳隆奇 Chang, Shu-Chiuan;Chen, Lung-Chi
Contributors:	應用數學系
Keywords:	DomanyâKinzel model;Directed percolation;Random walk;Asymptotic behavior;BerryâEsseen theorem;Large deviation
Date:	2015-10
Issue Date:	2016-01-13 16:22:46 (UTC+8)
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 Ï(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 xâ(0,1], yâ(0,1] and aspect ratio Î±=M/N fixed, we show that there is a critical value Î±c=(1âx+xy)(1+xâxy)/(xy2) such that as Nââ, Ï(M,N) is 1, 0 and 1/2 for Î±>Î±c, Î±<Î±c and Î±=Î±c, respectively. We also investigate the rate of convergence of Ï(M,N) and the asymptotic behavior of View the MathML source and View the MathML source where View the MathML source and View the MathML source as Nââ.
Relation:	Physica A, 436, 547-557
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1016/j.physa.2015.05.083
DOI:	10.1016/j.physa.2015.05.083
Appears in Collections:	[應用數學系] 期刊論文

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