Oriented Percolation On The N-scaled Sierpinski Carpet Lattice

The theory of Percolation has been heated studied in recent decades.It has been widely applied in physics and mathematics.Study of Percolation on Sierpi(?)ski carpet latice is very heat in recent years(See[1][10][11][12]).We focus on the study of a branch of Sierpi'nski carpet latice which is the oriented percolation of N-scaled Sierpi(?)ski in this paper.This paper consists of three chapters.In chapter 1,we introduce some basic knowledge of percolation,some results in this field these years and percolation models on Sierpi(?)ski carpet latice.We also provide some main methods in the research of percolation.Chapter 2 is devoted to the introduction of N-scaled Sierpi(?)ski carpet lattice,the oriented percolation of N-scaled Sierpi(?)ski and the main result in this paper.The proof of the result is shown in chapter 3.We give some discussions on the critical phenomenon of the oriented percolation on N-scale Sierpi(?)ski carpet latice.The inexistence of the phase will be proved,that is to say critical probability is l.