Quasi non-ergodicity for finite 1-D structures

Abstract: In 2004 one of us (Toom) presented a process with local interaction and discrete time, which, although one-dimensional, displayed some form of non-ergodicity. However, Toom’s system “shrinks ” and therefore has no finite analog. We propose a similar process, with continuos time. Monte Carlo simulation of this process showed the same form of non-ergodicity as Toom proved and in addition thet new process does not ‘’shrink ” for some values of parameters, which allows us to consider a similar process with a finite space. We estimated the boundary between the regiona, where our process is “ergodic ” vs. “non-ergodic ” and “shrink ” vs. “does not shrink.