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Zbl 0581.60093

Quelques compléments sur le processus des misanthropes et le processus "zéro-range". (French)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 21, 363-382 (1985). ISSN 0246-0203

The misanthrope process is an infinite particle system on the lattice ${\bbfZ}\sp d$, which was introduced by the second author, Z. Wahrscheinlichkeitstheor. Verw. Geb. 70, 509-523 (1985; Zbl 0554.60097)]. It generalizes the zero range process. In the mentioned paper invariant measures and convergence to them were studied. \par The present paper gives two additional results for the one-dimensional case. It is shown for the nearest neighbour misanthrope process that, if the initial distribution is translation invariant, ergodic and has a finite density, then the process converges to the ergodic invariant measure with the same density. Furthermore it is proved that, if the expectation of the jumps is zero, then all invariant measures are translation invariant. The proofs are based on coupling techniques.
[M.Mürmann]

MSC 2000:: *60K35 Interacting random processes
60J25 Markov processes with continuous parameter
60J75 Jump processes

Keywords: Andjel, E.; Cocoa-Thivent, C.; Roussignol, M; infinite particle system; invariant measures; nearest neighbour misanthrope process; coupling techniques

Citations: Zbl 0554.60097

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