The Annals of Applied Probability

Large deviations for the exclusion process with a slow bond

Tertuliano Franco and Adriana Neumann

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Abstract

We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value $N^{-1}$, where $N$ is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynamical large deviations estimates in the diffusive scaling. The main challenge here is the fact that the presence of the slow bond gives rise to Robin’s boundary conditions in the continuum, substantially complicating the large deviations scenario.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 6 (2017), 3547-3587.

Dates
Received: January 2015
Revised: February 2017
First available in Project Euclid: 15 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1513328708

Digital Object Identifier
doi:10.1214/17-AAP1287

Mathematical Reviews number (MathSciNet)
MR3737932

Zentralblatt MATH identifier
06848273

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]
Secondary: 60F10: Large deviations

Keywords
Large deviations exclusion process

Citation

Franco, Tertuliano; Neumann, Adriana. Large deviations for the exclusion process with a slow bond. Ann. Appl. Probab. 27 (2017), no. 6, 3547--3587. doi:10.1214/17-AAP1287. https://projecteuclid.org/euclid.aoap/1513328708


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References

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