### Abstract

We consider symmetric simple exclusion processes with L = ρ̄N^{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}_{1} δ_{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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-84 |

Number of pages | 84 |

Journal | Probability Theory and Related Fields |

Volume | 113 |

Issue number | 1 |

State | Published - Jan 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Statistics and Probability

### Cite this

*Probability Theory and Related Fields*,

*113*(1), 1-84.

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

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 113, no. 1, pp. 1-84.

}

TY - JOUR

T1 - Large deviations for the symmetric simple exclusion process in dimensions d ≥ 3

AU - Quastel, J.

AU - Rezakhanlou, F.

AU - Varadhan, Srinivasa

PY - 1999/1

Y1 - 1999/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000435295&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000435295&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000435295

VL - 113

SP - 1

EP - 84

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1

ER -