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

J. Quastel, F. Rezakhanlou, Srinivasa Varadhan

Research output: Contribution to journalArticle

Abstract

We consider symmetric simple exclusion processes with L = ρ̄Nd 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[∑L1 δxi(.)] 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.

Original languageEnglish (US)
Pages (from-to)1-84
Number of pages84
JournalProbability Theory and Related Fields
Volume113
Issue number1
StatePublished - Jan 1999

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Exclusion Process
Large Deviations
Self-diffusion
Large Deviation Principle
Rate Function
Empirical Process
Scaling Limit
Density Profile
Diffusion Coefficient
Hydrodynamics
Torus
Initial conditions
Random variable
Scaling
Arbitrary
Profile
Object
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Statistics and Probability

Cite this

Large deviations for the symmetric simple exclusion process in dimensions d ≥ 3. / Quastel, J.; Rezakhanlou, F.; Varadhan, Srinivasa.

In: Probability Theory and Related Fields, Vol. 113, No. 1, 01.1999, p. 1-84.

Research output: Contribution to journalArticle

Quastel, J, Rezakhanlou, F & Varadhan, S 1999, 'Large deviations for the symmetric simple exclusion process in dimensions d ≥ 3', Probability Theory and Related Fields, vol. 113, no. 1, pp. 1-84.
Quastel, J. ; Rezakhanlou, F. ; Varadhan, Srinivasa. / Large deviations for the symmetric simple exclusion process in dimensions d ≥ 3. In: Probability Theory and Related Fields. 1999 ; Vol. 113, No. 1. pp. 1-84.
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