May Wish To Move The Uniqueness Of The Percolation Critical Probability

Percolation model was first proposed by Broadbent S.R. and Hammersly J.M. in 1957.It has been to study in depth in the past 60 years .This statistical physics model of the probability expanded field of study ,and also provided a rigorous mathematical model based on this .In the first chapter,Let us go back to a percolation model of the Background ,and have a brief account of some of the classic percolation model knowledge and research .Then we introductioned the percolation model on the quasi-transitive graph and gave some results in the conditions of p > p_c. At last,this paper gave the theorem of the exponential decay of the radius distribution beneath p_c ,and the theorem of uniqueness of critical probability.In the second chapter,we introduced the related attenuation of formula and relevant knowledge inequality . Then we used the Russos formula ,BK inequality , some properties on the quasi-transitive graph and so on to prove the The results .