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題名 Asymptotic Behavior for a Version of Directed Percolation on the Square Lattice 作者 陳隆奇
Chen, Lung-Chi貢獻者 應數系 關鍵詞 Domany–Kinzel model;Directed percolation;Compact directed percolation;Asymptotic behavior;Critical behavior;Susceptibility;Exact solutions;Berry–Esseen theorem 日期 2011.03 上傳時間 13-Nov-2014 17:23:25 (UTC+8) 摘要 We consider a version of directed bond percolation on a square lattice whose vertical edges are directed upward with probabilities pvpv and horizontal edges are directed rightward with probabilities phph and 1 in alternate rows. Let τ(M,N)τ(M,N) be the probability that there is a connected directed path of occupied edges from (0,0)(0,0) to (M,N)(M,N). For each View the MathML sourceph∈[0,1],pv=(0,1) and aspect ratio α=M/Nα=M/N fixed, it was established (Chen and Wu, 2006) [9] that there is an View the MathML sourceαc=[1−pv2−ph(1−pv)2]/2pv2 such that, as N→∞N→∞, τ(M,N)τ(M,N) is 11, 00, and 1/21/2 for α>αcα>αc, α<αcα<αc, and α=αcα=αc, respectively. In particular, for ph=0ph=0 or 11, the model reduces to the Domany–Kinzel model (Domany and Kinzel, 1981 [7]). In this article, we investigate the rate of convergence of τ(M,N)τ(M,N) and the asymptotic behavior of View the MathML sourceτ(Mn−,N) and View the MathML sourceτ(Mn+,N), where View the MathML sourceMn−/N↑αc and View the MathML sourceMn+/N↓αc as N↑∞N↑∞. Moreover, we obtain a susceptibility on the rectangular net {(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}{(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}. The proof is based on the Berry–Esseen theorem. 關聯 Physica A, 390(3), 419-426 資料類型 article DOI http://dx.doi.org/10.1016/j.physa.2010.09.039 dc.contributor 應數系 en_US dc.creator (作者) 陳隆奇 zh_TW dc.creator (作者) Chen, Lung-Chi en_US dc.date (日期) 2011.03 en_US dc.date.accessioned 13-Nov-2014 17:23:25 (UTC+8) - dc.date.available 13-Nov-2014 17:23:25 (UTC+8) - dc.date.issued (上傳時間) 13-Nov-2014 17:23:25 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/71420 - dc.description.abstract (摘要) We consider a version of directed bond percolation on a square lattice whose vertical edges are directed upward with probabilities pvpv and horizontal edges are directed rightward with probabilities phph and 1 in alternate rows. Let τ(M,N)τ(M,N) be the probability that there is a connected directed path of occupied edges from (0,0)(0,0) to (M,N)(M,N). For each View the MathML sourceph∈[0,1],pv=(0,1) and aspect ratio α=M/Nα=M/N fixed, it was established (Chen and Wu, 2006) [9] that there is an View the MathML sourceαc=[1−pv2−ph(1−pv)2]/2pv2 such that, as N→∞N→∞, τ(M,N)τ(M,N) is 11, 00, and 1/21/2 for α>αcα>αc, α<αcα<αc, and α=αcα=αc, respectively. In particular, for ph=0ph=0 or 11, the model reduces to the Domany–Kinzel model (Domany and Kinzel, 1981 [7]). In this article, we investigate the rate of convergence of τ(M,N)τ(M,N) and the asymptotic behavior of View the MathML sourceτ(Mn−,N) and View the MathML sourceτ(Mn+,N), where View the MathML sourceMn−/N↑αc and View the MathML sourceMn+/N↓αc as N↑∞N↑∞. Moreover, we obtain a susceptibility on the rectangular net {(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}{(m,n)∈Z+×Z+:0≤m≤M and 0≤n≤N}. The proof is based on the Berry–Esseen theorem. en_US dc.format.extent 295316 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.relation (關聯) Physica A, 390(3), 419-426 en_US dc.subject (關鍵詞) Domany–Kinzel model;Directed percolation;Compact directed percolation;Asymptotic behavior;Critical behavior;Susceptibility;Exact solutions;Berry–Esseen theorem en_US dc.title (題名) Asymptotic Behavior for a Version of Directed Percolation on the Square Lattice en_US dc.type (資料類型) article en dc.identifier.doi (DOI) 10.1016/j.physa.2010.09.039 - dc.doi.uri (DOI) http://dx.doi.org/10.1016/j.physa.2010.09.039 -
