CONTACT PROCESS ON HEXAGONAL LATTICE  

作　　者：姚强 李群昌 

机构地区：[1]Department of Statistics and Actuarial Science, School of Finance and Statistics, East China Normal University [2]School of Mathematical Sciences, Peking University

出　　处：《Acta Mathematica Scientia》2010年第3期769-790,共22页数学物理学报（B辑英文版）

基　　金：Supported in part by the NNSF of China (10531070,10625101);the National Basic Research Program of China (2006CB805900)

摘　　要：In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

关 键 词：Hexagonal lattice contact process critical value complete convergence theorem rate of growth 

分 类 号：O157.5[理学—数学]