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Processus des misanthropes. (French) Zbl 0554.60097
We consider a system of identical interacting particles moving on the lattice \({\mathbb{Z}}^ d\). The rate at which a particle at the site x jumps to the site y is p(y-x)b(\(\eta\) (x),\(\eta\) (y)) where p is an irreducible probability on \({\mathbb{Z}}^ d\) and b(\(\eta\) (x),\(\eta\) (y)) is an increasing (resp. decreasing) function of the number \(\eta\) (x) (resp. \(\eta\) (y)) of particles at site x (resp. y). We study the convergence of the system to equilibrium and describe the invariant measures.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60B10 Convergence of probability measures
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