Occupation time large deviations of two-dimensional symmetric simple exclusion process

Abstract

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.