The Study Of Ergodicity For Biased Voter Model, Not Nearest-neighbor Exclusion Process And Hybrid Process

This paper was divided into four parts.In the first chapters, we intro-duced the ergodic ,recurrent,transient of the Markov chain and Lyapunov functions.In the second chapter ,we showed that discrete-time biased voter model is positive recurrent.For any initial configuration s and some 0 such that for In the third chapter,we showed that a finite range exclusion process isergodic for ;transient for In the last chapter,we showed that there exists such that for any q hybrid process is ergodic for all for any and hybrid process is ergodic.