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題名 Asymptotic behavior for a long-range Domany–Kinzel model 作者 Chang, Shu-Chiuan
陳隆奇
Chen, Lung-Chi貢獻者 應數系 關鍵詞 Keywords: Domany–Kinzel model; Directed percolation; Random walk; Asymptotic behavior; Critical behavior; Berry–Esseen theorem; Large deviation 日期 2018-09 上傳時間 25-Jul-2018 14:27:49 (UTC+8) 摘要 We consider a long-range Domany–Kinzel model proposed by Li and Zhang (1983), such that for every site (i,j) in a two-dimensional rectangular lattice there is a directed bond present from site (i,j) to (i+1,j) with probability one. There are also m+1 directed bounds present from (i,j) to (i−k+1,j+1), k=0,1,…,m with probability pk∈[0,1), where m is a non-negative integer. Let τm(M,N) be the probability that there is at least one connected-directed path of occupied edges from (0,0) to (M,N). Defining the aspect ratio α=M∕N, we derive the correct critical value αm,c∈R such that as N→∞, τm(M,N) converges to 1, 0 and 1∕2 for α>αm,c, α<αm,c and α=αm,c, respectively, and we study the rate of convergence. Furthermore, we investigate the cases in the infinite m limit. Specifically, we discuss in details the case such that pn∈[0,1) with n∈Z+ and pn≈n→∞pn−s for p∈(0,1) and s>0. We find that the behavior of limm→∞τm(M,N) for this case highly depends on the value of s and how fast one approaches to the critical aspect ratio. The present study corrects and extends the results given in Li and Zhang (1983). 關聯 Physica A: Statistical Mechanics and its Applications,Volume 506, Pages 112-127 資料類型 article DOI https://doi.org/10.1016/j.physa.2018.03.061 dc.contributor 應數系 - dc.creator (作者) Chang, Shu-Chiuan en_US dc.creator (作者) 陳隆奇 zh_TW dc.creator (作者) Chen, Lung-Chi en_US dc.date (日期) 2018-09 - dc.date.accessioned 25-Jul-2018 14:27:49 (UTC+8) - dc.date.available 25-Jul-2018 14:27:49 (UTC+8) - dc.date.issued (上傳時間) 25-Jul-2018 14:27:49 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/118891 - dc.description.abstract (摘要) We consider a long-range Domany–Kinzel model proposed by Li and Zhang (1983), such that for every site (i,j) in a two-dimensional rectangular lattice there is a directed bond present from site (i,j) to (i+1,j) with probability one. There are also m+1 directed bounds present from (i,j) to (i−k+1,j+1), k=0,1,…,m with probability pk∈[0,1), where m is a non-negative integer. Let τm(M,N) be the probability that there is at least one connected-directed path of occupied edges from (0,0) to (M,N). Defining the aspect ratio α=M∕N, we derive the correct critical value αm,c∈R such that as N→∞, τm(M,N) converges to 1, 0 and 1∕2 for α>αm,c, α<αm,c and α=αm,c, respectively, and we study the rate of convergence. Furthermore, we investigate the cases in the infinite m limit. Specifically, we discuss in details the case such that pn∈[0,1) with n∈Z+ and pn≈n→∞pn−s for p∈(0,1) and s>0. We find that the behavior of limm→∞τm(M,N) for this case highly depends on the value of s and how fast one approaches to the critical aspect ratio. The present study corrects and extends the results given in Li and Zhang (1983). en_US dc.format.extent 432412 bytes - dc.format.mimetype application/pdf - dc.relation (關聯) Physica A: Statistical Mechanics and its Applications,Volume 506, Pages 112-127 - dc.subject (關鍵詞) Keywords: Domany–Kinzel model; Directed percolation; Random walk; Asymptotic behavior; Critical behavior; Berry–Esseen theorem; Large deviation en_US dc.title (題名) Asymptotic behavior for a long-range Domany–Kinzel model en_US dc.type (資料類型) article - dc.identifier.doi (DOI) 10.1016/j.physa.2018.03.061 - dc.doi.uri (DOI) https://doi.org/10.1016/j.physa.2018.03.061 -
