# Large deviations of a tracer in the symmetric exclusion process

Abstract : The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite lattice with a step initial profile with average densities $\rho_{+}$ and $\rho_{-}$ on the right and on the left of the origin. When $\rho_{+} = \rho_{-}$, the gas is at equilibrium and undergoes stationary fluctuations. When these densities are unequal, the gas is out of equilibrium and will remain so forever. A tracer, or a tagged particle, is initially located at the boundary between the two domains; its position $X_t$ is a random observable in time, that carries information on the non-equilibrium dynamics of the whole system. We derive an exact formula for the cumulant generating function and the large deviation function of $X_t$, in the long time limit, and deduce the full statistical properties of the tracer's position. The equilibrium fluctuations of the tracer's position, when the density is uniform, are obtained as an important special case.
Document type :
Journal articles
Domain :
Complete list of metadatas

https://hal-cea.archives-ouvertes.fr/cea-01484620
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, March 7, 2017 - 2:51:17 PM
Last modification on : Monday, February 10, 2020 - 6:13:40 PM
Long-term archiving on: : Thursday, June 8, 2017 - 2:01:05 PM

### File

1702.05824.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : cea-01484620, version 1
• ARXIV : 1702.05824

### Citation

T. Imamura, K. Mallick, T. Sasamoto. Large deviations of a tracer in the symmetric exclusion process. Physical Review Letters, American Physical Society, 2017, 118, pp.160601. ⟨cea-01484620⟩

Record views