We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density $\rho$. We prove that for dimension $d=2$ the occupation time of the site 0 is diffusive as soon as $\rho\neq 1/2$. For dimension $d=1$, if the density $\rho$ is equal to $1/2$, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as $t^{5/4}$.
Publié le : 2004-01-14
Classification:
Exclusion process,
occupation time of a site,
invariance principle,
60K35,
60F05
@article{1079021466,
author = {Bernardin, C\'edric},
title = {Fluctuations in the occupation time of a site in the asymmetric simple exclusion process},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 855-879},
language = {en},
url = {http://dml.mathdoc.fr/item/1079021466}
}
Bernardin, Cédric. Fluctuations in the occupation time of a site in the asymmetric simple exclusion process. Ann. Probab., Tome 32 (2004) no. 1A, pp. 855-879. http://gdmltest.u-ga.fr/item/1079021466/