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SUMMARY:Large deviations for out of equilibrium correlations in the  symme
 tric simple exclusion process - Benoit Dagallier (Statslab)
DTSTART:20230221T140000Z
DTEND:20230221T150000Z
UID:TALK197662@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:For finite size Markov chains\, the probability that a \ntime-
 averaged observable take an anomalous value in the long time limit \nwas q
 uantified in a celebrated result by Donsker and Varadhan. In the \nstudy o
 f interacting particle systems\, one is interested not only in the \nlarge
  time limit\, but also in large system sizes. In this second limit\, \nobs
 ervables of the chain each live at different scales\, and \nunderstanding 
 how scales decouple is necessary to take the limit.\nIn a joint work with 
 Thierry Bodineau \n(https://arxiv.org/abs/2212.11561)\, we study a paradig
 matic example of \nout of equilirium interacting particle systems: the one
 -dimensional \nsymmetric simple exclusion process connected with reservoir
 s of \nparticles at different density. We focus on the scale of two point 
 \ncorrelations and obtain the long time\, large system size limits on the 
 \nprobability of observing anomalous correlations. This is done through \n
 quantitative\, non-asymptotic estimates at the level of the dynamics. The 
 \nkey ingredient is a precise approximation of the dynamics and its \ninva
 riant measure (not explicitly known)\, that is of independent \ninterest. 
 The quality of this approximation is controlled through \nrelative entropy
  bounds\, making use of recent results of Jara and \nMenezes (https://arxi
 v.org/abs/1810.09526).
LOCATION:MR12\, Centre for Mathematical Sciences
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