## The Annals of Probability

### 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.

#### Article information

Source
Ann. Probab., Volume 32, Number 1B (2004), 661-691.

Dates
First available in Project Euclid: 11 March 2004

https://projecteuclid.org/euclid.aop/1079021460

Digital Object Identifier
doi:10.1214/aop/1079021460

Mathematical Reviews number (MathSciNet)
MR2039939

Zentralblatt MATH identifier
1061.60103

Subjects
Primary: 60F10: Large deviations

#### Citation

Chang, Chih-Chung; Landim, Claudio; Lee, Tzong-Yow. Occupation time large deviations of two-dimensional symmetric simple exclusion process. Ann. Probab. 32 (2004), no. 1B, 661--691. doi:10.1214/aop/1079021460. https://projecteuclid.org/euclid.aop/1079021460

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