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題名 Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice 作者 陳隆奇
Chen, Lung-Chi
Chang, Shu-Chiuan貢獻者 應數系 關鍵詞 Domany–Kinzel; model; Directed percolation; Random walk; Asymptotic behavior; Berry–Esseen theorem; Large deviation 日期 2014-05 上傳時間 13-Jan-2016 16:23:26 (UTC+8) 摘要 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↑∞. 關聯 Journal of Statistical Physics, 155(3), 500-522 資料類型 article DOI http://dx.doi.org/10.1007/s10955-014-0961-7 dc.contributor 應數系 - dc.creator (作者) 陳隆奇 zh_TW dc.creator (作者) Chen, Lung-Chi en_US dc.creator (作者) Chang, Shu-Chiuan en_US dc.date (日期) 2014-05 - dc.date.accessioned 13-Jan-2016 16:23:26 (UTC+8) - dc.date.available 13-Jan-2016 16:23:26 (UTC+8) - dc.date.issued (上傳時間) 13-Jan-2016 16:23:26 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/80556 - dc.description.abstract (摘要) 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↑∞. - dc.format.extent 535866 bytes - dc.format.mimetype application/pdf - dc.relation (關聯) Journal of Statistical Physics, 155(3), 500-522 - 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 Triangular Lattice - dc.type (資料類型) article - dc.identifier.doi (DOI) 10.1007/s10955-014-0961-7 - dc.doi.uri (DOI) http://dx.doi.org/10.1007/s10955-014-0961-7 -
