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CATEGORIES:Probability
SUMMARY:Large deviations for out of equilibrium correlatio
ns in the symmetric simple exclusion process - Be
noit Dagallier (Statslab)
DTSTART;TZID=Europe/London:20230221T140000
DTEND;TZID=Europe/London:20230221T150000
UID:TALK197662AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/197662
DESCRIPTION:For finite size Markov chains\, the probability th
at a \ntime-averaged observable take an anomalous
value in the long time limit \nwas quantified in a
celebrated result by Donsker and Varadhan. In the
\nstudy of interacting particle systems\, one is
interested not only in the \nlarge time limit\, bu
t also in large system sizes. In this second limit
\, \nobservables of the chain each live at differe
nt scales\, and \nunderstanding how scales decoupl
e is necessary to take the limit.\nIn a joint work
with Thierry Bodineau \n(https://arxiv.org/abs/22
12.11561)\, we study a paradigmatic example of \no
ut of equilirium interacting particle systems: the
one-dimensional \nsymmetric simple exclusion proc
ess connected with reservoirs of \nparticles at di
fferent density. We focus on the scale of two poin
t \ncorrelations and obtain the long time\, large
system size limits on the \nprobability of observi
ng anomalous correlations. This is done through \n
quantitative\, non-asymptotic estimates at the lev
el of the dynamics. The \nkey ingredient is a prec
ise approximation of the dynamics and its \ninvari
ant measure (not explicitly known)\, that is of in
dependent \ninterest. The quality of this approxim
ation is controlled through \nrelative entropy bou
nds\, making use of recent results of Jara and \nM
enezes (https://arxiv.org/abs/1810.09526).
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Perla Sousi
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