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Zbl 0978.60105
Belitsky, Vladimir; Ferrari, Pablo A.; Menshikov, Mikhail V.; Popov, Serguei Yu.
A mixture of the exclusion process and the voter model. (English)
[J] Bernoulli 7, No. 1, 119-144 (2001). ISSN 1350-7265

A mixture of the simple exclusion process and the voter model of one-dimensional nearest-neighbour interacting particle systems is studied. The new model is described by two parameters, a transition rate in the exclusion part and a mixture parameter of the exclusion and voter parts. The main result, which is quite complete, describes the ergodic and transient regions of the parameters for the process. The main tool is the recent result on the ergodicity, recurrence and transience of Markov chains developed by V. A. Malyshev et al.
[Chen Mu-Fa (Beijing)]

MSC 2000:: *60K35 Interacting random processes

Keywords: exclusion process; Lyapunov function; voter model

Cited in: Zbl 1209.60054

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