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Large deviations for out of equilibrium correlations in the symmetric simple exclusion process

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For finite size Markov chains, the probability that a time-averaged observable take an anomalous value in the long time limit was quantified in a celebrated result by Donsker and Varadhan. In the study of interacting particle systems, one is interested not only in the large time limit, but also in large system sizes. In this second limit, observables of the chain each live at different scales, and understanding how scales decouple is necessary to take the limit. In a joint work with Thierry Bodineau (, we study a paradigmatic example of out of equilirium interacting particle systems: the one-dimensional symmetric simple exclusion process connected with reservoirs of particles at different density. We focus on the scale of two point correlations and obtain the long time, large system size limits on the probability of observing anomalous correlations. This is done through quantitative, non-asymptotic estimates at the level of the dynamics. The key ingredient is a precise approximation of the dynamics and its invariant measure (not explicitly known), that is of independent interest. The quality of this approximation is controlled through relative entropy bounds, making use of recent results of Jara and Menezes (

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