Random Permutation Graphs And Markov Chain Links

We mainly investigate in this papar the property of random permutation with n nodes. In 2001, Bela,Bollobas wrote a book, its name is 《 Random Graphs 》 . The book introduce a theorem about the probability that a fixed classs of finite non-intersected subsets of nodes are located in different components. And it has a useful deduction. Illumined from the article of Chen,X.,Ying,J., Random mapping graphs and Markov chains, preprint, we can use this deduction to construct a scheme of allocating particles and prove this scheme is a Markov chain. We also can prove some behaviors of random permutation may be represented in the Markov chain in certain sense. Finally, we find the limit associated distributing about the connection component of random permutation.Theorem: We define H_n~k(σ), σ ∈ Ω_n, the number of nodes in the k-th connection component.when n goes to infinity,the distring of (H_n~1/n,…,H_n~k/n,…) convergece to the distributingof , where are i.i.d. with [0,1] uniformity distribution.