%0 Journal Article
%T Convergence rate in a martingale CLT for percolation clusters<br>渗流簇中鞅中心极限定理的收敛速度
%A JIANG Jian-Ping
%A ZHANG San-Guo
%A GUO Tian-De
%A <br>姜建平
%A 张三国
%A 郭田德
%J 中国科学院研究生院学报
%D 2010
%I 
%X Consider bond percolation on Zd with parameter p. Let Kn be the number of open clusters in -n,n]d. We investigate the convergence rate in the martingaleCLT for Kn. Generally, the best convergence rate for classicalmartingale CLT is O(n-d/2), and our result is Pp((Kn-Ep(Kn))/(Varp(Kn))) ≤x =x∫-∞(1/(2π)) e(-y2)/2dy+o(n-d/2 +ε0) for all x, where ε0 is any constant real number in 0, d/2 . As far as we know, this is the first convergence rate in CLTs for percolation.
%K percolation
%K martingale
%K central limit theorem
%K rate of convergence<br>渗流
%K 鞅
%K 中心极限定理
%K 收敛速度
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=B5EDD921F3D863E289B22F36E70174A7007B5F5E43D63598017D41BB67247657&cid=B47B31F6349F979B&jid=67CDFDECD959936E166E0F72DE972847&aid=589F7140F8F8A8B7210011AA08033678&yid=140ECF96957D60B2&vid=DB817633AA4F79B9&iid=94C357A881DFC066&sid=52B9DFFFCC2EB041&eid=7882A2973AA04DE8&journal_id=1002-1175&journal_name=中国科学院研究生院学报&referenced_num=0&reference_num=19