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.