# zbMATH — the first resource for mathematics

An ergodic theorem for generalized simple exclusion processes with reversible positive transition. (English) Zbl 0644.60110
This paper is devoted to the ergodic theory of a generalized simple exclusion process with the state space $$\{0,1,...,m\}^ S$$ (m$$\geq 1$$, S is a countable set) and a reversible positive recurrent transition probability matrix $$P=(p(x,y))_{x,y\in S}$$. Referring T. M. Ligett, Ann. Probab. 2, 989-998 (1974; Zbl 0295.60086), the set of its invariant probability measures are described and the ergodic properties of the process are obtained.
We also prove that the set of its reversible probability measures coincides with the set of its invariant probability measures. So the main results of F. Spitzer, Adv. Math. 5, 246-290 (1970; Zbl 0312.60060), are extended.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60F15 Strong limit theorems