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SUMMARY:Mean field limits for weakly interacting diffusions: phase transit
ions\, multiscale analysis\, metastability and inference
DTSTART;VALUE=DATE-TIME:20230207T130000Z
DTEND;VALUE=DATE-TIME:20230207T140000Z
DTSTAMP;VALUE=DATE-TIME:20230324T185400Z
UID:indico-event-8856@indico.math.cnrs.fr
DESCRIPTION:Speakers: Greg Pavliotis\n\nWe consider a system of N weakly i
nteracting particles driven by white noise. The mean-field limit of this s
ystem is described by the (nonlinear and nonlocal) McKean-Vlasov-Fokker-Pl
anck PDE . We present a detailed analysis of continuous and discontinuous
phase transitions for theMcKeanVlasov PDE on the torus. We study the combi
ned diffusive/mean-field limit of systems of weakly interacting diffusions
with a periodic interaction potential. We show that\, in the presence of
phase transitions\, the two limits do not commute. We then show the equiva
lence between uniformpropagation of chaos\, a uniform-in-N Logarithmic Sob
olev inequality\, the absence of phase transitions for the mean-field limi
t\, and of Gaussian fluctuations around the McKean-Vlasov PDE . We discuss
about dynamical metastability for systems that exhibit discontinuous phas
e transitions.Finally\, we develop inference methodologies for estimating
parameters in the drift of the McKean SDE using either the stochastic grad
ient descent algorithm or eigenfunction martingale estimators.\n\nhttps://
indico.math.cnrs.fr/event/8856/
URL:https://indico.math.cnrs.fr/event/8856/
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