A Class With Sierpi (?) Ski Carpet Quasi-transitive Graph On The Percolation Model

Percolation model was firstly proposed by Broadbent S.R. and Hammersly J.M. in 1957.This not only extends the research fields of probability , but also provides strict basis for Stat. Physics.We consider the percolation on quasi-itransitive graph connected with Sierpinski Carpet in the article. In Chapter 1, we review the study progress on some percolation models such as the percolation on Z~d and some lattice fractals at first,and we introduce the Sierpinski Carpet.Then we give the study idea in this article.At last, we present the basic definitions and lemma which are used in Chapter 2.In Chapter 2,we use the enhancement theory,the square root technique,RSW lemma,ACCFR lemma ,probability and measure to study the percolation on quasi-transitive graph connected with Sierpinski Carpet including continuity of the critical probability,the uniqueness of infinite clusters and the exponential decays of connectivity functions, and we give out the strict provement .Then we prove that the graphs with different, isoperimetric dimensions can have the same critical probability.