Probability Theory and Related Fields

, Volume 113, Issue 1, pp 1–84 | Cite as

Large deviations for the symmetric simple exclusion process in dimensions d≥ 3

  • J. Quastel
  • F. Rezakhanlou
  • S. R. S. Varadhan
Article

Abstract.

We consider symmetric simple exclusion processes with L=&ρmacr;Nd 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, Nd[∑L1δxi(·)] 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.

Mathematics Subject Classification (1991): 60K35 (60F10) 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • J. Quastel
    • 1
  • F. Rezakhanlou
    • 2
  • S. R. S. Varadhan
    • 3
  1. 1.Department of Mathematics, University of California, Davis, CA 95616. Present address: Departments of Mathematics and Statistics, University of Toronto, 100 St. George Street, Toronto, Ontario, M5S 3G3, Canada. Partially supported by NSF grant DMS-9504791CA
  2. 2.Department of Mathematics, University of California, Berkeley, CA 94720. Partially supported by NSF grant DMS-9424270
  3. 3.Courant Institute, 251 Mercer St., New York, NY 10012. Partially supported by NSF grant DMS-9503419 and ARO grant DAAH04-95-1-0666

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