## Stationary product measures for conservative particle systems and ergodicity criteria.(English)Zbl 1286.60095

The paper investigates the stationary and ergodic measures for the exclusion-inclusion-, zero range-misanthrope process. Finding all the ergodic measures for such systems is still an open problem, and here, it is shown that this question can be dealt with irrespective of the characteristics of the model. Broadly speaking, the main result can be summarized as follows. When the generator of the system generates a Markov process, then the measure is ergodic if the $$\sigma$$ algebra of the sets, which are invariant under transformations of the process defined by the generator, is trivial.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G10 Stationary stochastic processes 82C22 Interacting particle systems in time-dependent statistical mechanics 60G50 Sums of independent random variables; random walks
Full Text: