We prove a large deviations principle for the occupation time of a site in the two-dimensional symmetric simple exclusion process. The decay probability rate is of order $t/\log t$ and the rate function is given by $\Upsilon_\alpha (\beta) = (\pi/2) \{\sin^{-1}(2\beta-1)-\sin^{-1}(2\alpha -1) \}^2$. The proof relies on a large deviations principle for the polar empirical measure which contains an interesting $\log$ scale spatial average. A contraction principle permits us to deduce the occupation time large deviations from the large deviations for the polar empirical measure.
Publié le : 2004-01-14
Classification:
Exclusion process,
hydrodynamic limit,
large deviations,
occupation time,
60F10
@article{1079021460,
author = {Chang, Chih-Chung and Landim, Claudio and Lee, Tzong-Yow},
title = {Occupation time large deviations of two-dimensional symmetric simple exclusion process},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 661-691},
language = {en},
url = {http://dml.mathdoc.fr/item/1079021460}
}
Chang, Chih-Chung; Landim, Claudio; Lee, Tzong-Yow. Occupation time large deviations of two-dimensional symmetric simple exclusion process. Ann. Probab., Tome 32 (2004) no. 1A, pp. 661-691. http://gdmltest.u-ga.fr/item/1079021460/