Summary
We consider a system of identical interacting particles moving on the lattice ℤd. The rate at which a particle at the site x jumps to the site y is p(y−x)b(η(x), η(y)) where p is an irreducible probability on ℤd and b(η(x), η(y)) is an increasing (resp. decreasing) function of the number η(x) (resp. η(y)) of particles at site x (resp. y). We study the convergence of the system to equilibrium and describe the invariant measures.
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Cocozza-Thivent, C. Processus des misanthropes. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 509–523 (1985). https://doi.org/10.1007/BF00531864
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DOI: https://doi.org/10.1007/BF00531864