Spectral Gap for Open Jackson Networks  

作　　者：Yong Hua MAO Liang Hui XIA 

机构地区：[1]School of Mathematical Sciences,LMCS,Ministry of Education Beijing Normal University [2]Department of Mathematics,Ji'nan University

出　　处：《Acta Mathematica Sinica,English Series》2015年第12期1879-1894,共16页数学学报（英文版）

基　　金：Supported in part by 985 Project;973 Project(Grant No.2011CB808000);NSFC(Grant No.11131003);SRFDP(Grant No.20100003110005);the Fundamental Research Funds for the Central Universities

摘　　要：We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization procedure.The upper bound of the spectral gap is also presented.We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization procedure.The upper bound of the spectral gap is also presented.

关 键 词：Jackson networks REVERSIBILITY decomposition of Markov chain spectral gap SYMMETRIZATION 

分 类 号：O211.62[理学—概率论与数理统计]