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

### With Benoit Dagallier (Statslab)

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

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

(https://arxiv.org/abs/2212.11561), 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 (https://arxiv.org/abs/1810.09526).

- Speaker: Benoit Dagallier (Statslab)
- Tuesday 21 February 2023, 14:00–15:00
- Venue: MR12, Centre for Mathematical Sciences.
- Series: Probability; organiser: Perla Sousi.