Please use this identifier to cite or link to this item: `https://ah.nccu.edu.tw/handle/140.119/71420`

 Title: Asymptotic Behavior for a Version of Directed Percolation on the Square Lattice Authors: 陳隆奇Chen, Lung-Chi Contributors: 應數系 Keywords: Domany–Kinzel model;Directed percolation;Compact directed percolation;Asymptotic behavior;Critical behavior;Susceptibility;Exact solutions;Berry–Esseen theorem Date: 2011.03 Issue Date: 2014-11-13 17:23:25 (UTC+8) Abstract: 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)  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 ). 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. Relation: Physica A, 390(3), 419-426 Data Type: article DOI 連結: http://dx.doi.org/10.1016/j.physa.2010.09.039 Appears in Collections: [應用數學系] 期刊論文

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