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CATEGORIES:Applied and Computational Analysis
SUMMARY:Mean field limits for weakly interacting diffusion
 s: phase transitions\, multiscale analysis\, metas
 tability and inference - Greg Pavliotis - Imperial
  College
DTSTART;TZID=Europe/London:20221201T150000
DTEND;TZID=Europe/London:20221201T160000
UID:TALK192068AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/192068
DESCRIPTION:We consider a system of N weakly interacting parti
 cles driven by white noise. The mean-field limit o
 f this system is described by the (nonlinear and n
 onlocal) McKean-Vlasov-Fokker-Planck PDE. We prese
 nt a detailed analysis of continuous and discontin
 uous phase transitions for the McKeanVlasov PDE on
  the torus. We study the combined diffusive/mean-f
 ield limit of systems of weakly interacting diffus
 ions with a periodic interaction potential. We sho
 w that\, in the presence of phase transitions\, th
 e two limits do not commute. We then show the equi
 valence between uniform propagation of chaos\, a u
 niform-in-N Logarithmic Sobolev inequality\, the a
 bsence of phase transitions for the mean-field lim
 it\, and of Gaussian fluctuations around the McKea
 n-Vlasov PDE. We discuss about dynamical metastabi
 lity for systems that exhibit discontinuous phase 
 transitions. Finally\, we develop inference method
 ologies for estimating parameters in the drift of 
 the McKean SDE using either the stochastic gradien
 t descent algorithm or eigenfunction martingale es
 timators.\n\n 
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Edriss S. Titi
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