Long-range exclusion processes, generator and invariant measures
Andjel, Enrique D. ; Guiol, Hervé
Ann. Probab., Tome 33 (2005) no. 1, p. 2314-2354 / Harvested from Project Euclid
We show that if μ is an invariant measure for the long range exclusion process putting no mass on the full configuration, L is the formal generator of that process and f is a cylinder function, then Lf∈L1(dμ) and ∫Lf dμ=0. This result is then applied to determine (i) the set of invariant and translation-invariant measures of the long range exclusion process on ℤd when the underlying random walk is irreducible; (ii) the set of invariant measures of the long range exclusion process on ℤ when the underlying random walk is irreducible and either has zero mean or allows jumps only to the nearest-neighbors.
Publié le : 2005-11-14
Classification:  Long range exclusion process,  ergodic theorems,  non-Feller process,  invariant measures,  60K35
@article{1133965860,
     author = {Andjel, Enrique D. and Guiol, Herv\'e},
     title = {Long-range exclusion processes, generator and invariant measures},
     journal = {Ann. Probab.},
     volume = {33},
     number = {1},
     year = {2005},
     pages = { 2314-2354},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1133965860}
}
Andjel, Enrique D.; Guiol, Hervé. Long-range exclusion processes, generator and invariant measures. Ann. Probab., Tome 33 (2005) no. 1, pp.  2314-2354. http://gdmltest.u-ga.fr/item/1133965860/