%0 Journal Article
%T Long-range exclusion processes, generator and invariant measures
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ TIMB
%A Andjel, Enrique D.
%A Guiol, Hervé
%Z Published at http://dx.doi.org/10.1214/009117905000000486 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
%< avec comité de lecture
%@ 0091-1798
%J Annals of Probability
%I Institute of Mathematical Statistics
%V 33
%N 6
%P 2314-2354
%8 2005-10-03
%D 2005
%Z math/0411655
%K Long range exclusion process
%K invariant measures
%K non Feller Process
%Z MCS : 60K35 ; 82C22
%Z Mathematics [math]/Probability [math.PR]
%Z Mathematics [math]/Mathematical Physics [math-ph]
%Z Physics [physics]/Mathematical Physics [math-ph]Journal articles
%X We show that if $\mu$ 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 $Lf\in\mathbf{L}^1(d\mu)$ and $\int Lf d\mu=0$. This result is then applied to determine (i) the set of invariant and translation-invariant measures of the long range exclusion process on $\mathbb{Z}^d$ when the underlying random walk is irreducible; (ii) the set of invariant measures of the long range exclusion process on $\mathbb{Z}$ when the underlying random walk is irreducible and either has zero mean or allows jumps only to the nearest-neighbors.
%G English
%L hal-00273600
%U https://hal.science/hal-00273600
%~ UGA
%~ IMAG
%~ LATP
%~ CNRS
%~ UNIV-GRENOBLE1
%~ UNIV-AMU
%~ INPG
%~ TIMC-IMAG
%~ I2M
%~ TDS-MACS
%~ UNIV-LYON