Abstract.
We consider symmetric simple exclusion processes with L=&ρmacr;N d particles in a periodic d-dimensional lattice of width N. We perform the diffusive hydrodynamic scaling of space and time. The initial condition is arbitrary and is typically far away form equilibrium. It specifies in the scaling limit a density profile on the d-dimensional torus. We are interested in the large deviations of the empirical process, N − d[∑L 1δ xi (·)] as random variables taking values in the space of measures on D[0.1]. We prove a large deviation principle, with a rate function that is more or less universal, involving explicity besides the initial profile, only such canonical objects as bulk and self diffusion coefficients.
Author information
Authors and Affiliations
Additional information
Received: 7 September 1997 / Revised version: 15 May 1998
Rights and permissions
About this article
Cite this article
Quastel, J., Rezakhanlou, F. & Varadhan, S. Large deviations for the symmetric simple exclusion process in dimensions d≥ 3. Probab Theory Relat Fields 113, 1–84 (1999). https://doi.org/10.1007/s004400050202
Issue Date:
DOI: https://doi.org/10.1007/s004400050202
- Mathematics Subject Classification (1991): 60K35 (60F10)