Multi-Type Directed Scale-Free Percolation

作     者：SHANG Yi-Lun 

作者机构：Institute for Cyber SecurityUniversity of Texas at San AntonioTexas 78249USA 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2012年第57卷第4期

页      面：701-716页

核心收录：

学科分类：03[法学] 080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0837[工学-安全科学与工程] 0838[工学-公安技术] 0306[法学-公安学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：long-range percolation random graph phase transition directed percolation regularly varying chemical distance 

摘      要：In this paper,we study a long-range percolation model on the lattice Z d with multi-type vertices and directed *** vertex x ∈ Z d is independently assigned a non-negative weight Wx and a type ψx,where(Wx) x∈Z d are *** variables,and(ψx) x∈Z d are also *** on weights and types,and given λ,α 0,the edges are independent and the probability that there is a directed edge from x to y is given by pxy = 1 exp(λφψ x ψ y WxWy /| x-y | α),where φij s are entries from a type matrix Φ.We show that,when the tail of the distribution of Wx is regularly varying with exponent τ-1,the tails of the out/in-degree distributions are both regularly varying with exponent γ = α(τ-1) /*** formulate conditions under which there exist critical values λ WCC c ∈(0,∞) and λ SCC c ∈(0,∞) such that an infinite weak component and an infinite strong component emerge,respectively,when λ exceeds them.A phase transition is established for the shortest path lengths of directed and undirected edges in the infinite component at the point γ = 2,where the out/in-degrees switch from having finite to infinite *** random graph model studied here features some structures of multi-type vertices and directed edges which appear naturally in many real-world networks,such as the SNS networks and computer communication networks.