Probability Theory and Related Fields

, Volume 171, Issue 3–4, pp 865–915

# Explicit LDP for a slowed RW driven by a symmetric exclusion process

Article

## Abstract

We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. These components have different structures (Gaussian and Poissonian, respectively) and to overcome this difficulty we make use of the theory of Orlicz spaces. In particular, the component of the rate function corresponding to the RW is explicit.

## Keywords

Large deviations Random environments Hydrodynamic limits Particle systems Exclusion process

## Mathematics Subject Classification

60F10 82C22 82D30

## Notes

### Acknowledgements

L.A. has been supported by NWO Gravitation Grant 024.002.003-NETWORKS. M.J. has been partially supported by the ERC Horizon 2020 grant #715734 and by NWO Gravitation Grant 024.002.003-NETWORKS.

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