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SUMMARY:Mean field limits for weakly interacting diffusions: phase transit
 ions\, multiscale analysis\, metastability and inference - Greg Pavliotis 
 - Imperial College
DTSTART:20221201T150000Z
DTEND:20221201T160000Z
UID:TALK192068@talks.cam.ac.uk
CONTACT:Edriss S. Titi
DESCRIPTION:We consider a system of N weakly interacting particles driven 
 by white noise. The mean-field limit of this system is described by the (n
 onlinear and nonlocal) McKean-Vlasov-Fokker-Planck PDE. We present a detai
 led analysis of continuous and discontinuous phase transitions for the McK
 eanVlasov PDE on the torus. We study the combined diffusive/mean-field lim
 it 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 equivalence between uniform propag
 ation of chaos\, a uniform-in-N Logarithmic Sobolev inequality\, the absen
 ce of phase transitions for the mean-field limit\, and of Gaussian fluctua
 tions around the McKean-Vlasov PDE. We discuss about dynamical metastabili
 ty for systems that exhibit discontinuous phase transitions. Finally\, we 
 develop inference methodologies for estimating parameters in the drift of 
 the McKean SDE using either the stochastic gradient descent algorithm or e
 igenfunction martingale estimators.\n\n 
LOCATION:Centre for Mathematical Sciences\, MR14
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