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題名 Asymptotic behavior for a version of directed percolation on the honeycomb lattice
作者 張書銓; 陳隆奇
Chang, Shu-Chiuan;Chen, Lung-Chi
貢獻者 應用數學系
關鍵詞 Domany–Kinzel model; Directed percolation; Random walk; Asymptotic behavior; Berry–Esseen theorem; Large deviation
日期 2015-10
上傳時間 13-一月-2016 16:22:46 (UTC+8)
摘要 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 View the MathML source and View the MathML source where View the MathML source and View the MathML source as N↑∞.
關聯 Physica A, 436, 547-557
資料類型 article
DOI http://dx.doi.org/10.1016/j.physa.2015.05.083
dc.contributor 應用數學系-
dc.creator (作者) 張書銓; 陳隆奇zh_TW
dc.creator (作者) Chang, Shu-Chiuan;Chen, Lung-Chi-
dc.date (日期) 2015-10-
dc.date.accessioned 13-一月-2016 16:22:46 (UTC+8)-
dc.date.available 13-一月-2016 16:22:46 (UTC+8)-
dc.date.issued (上傳時間) 13-一月-2016 16:22:46 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/80553-
dc.description.abstract (摘要) 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 View the MathML source and View the MathML source where View the MathML source and View the MathML source as N↑∞.-
dc.format.extent 548600 bytes-
dc.format.mimetype application/pdf-
dc.relation (關聯) Physica A, 436, 547-557-
dc.subject (關鍵詞) Domany–Kinzel model; Directed percolation; Random walk; Asymptotic behavior; Berry–Esseen theorem; Large deviation-
dc.title (題名) Asymptotic behavior for a version of directed percolation on the honeycomb lattice-
dc.type (資料類型) article-
dc.identifier.doi (DOI) 10.1016/j.physa.2015.05.083-
dc.doi.uri (DOI) http://dx.doi.org/10.1016/j.physa.2015.05.083-