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SUMMARY:Phase transitions\, logarithmic Sobolev inequalities\, and uniform
 -in-time propagation of chaos for weakly interacting diffusions - Matias G
 onzalo Delgadino (University of Texas at Austin)
DTSTART:20220222T145000Z
DTEND:20220222T153500Z
UID:TALK170420@talks.cam.ac.uk
DESCRIPTION:In this talk\, we will study the mean field limit of weaklyint
 eracting diffusions for confining and interaction potentials thatare not n
 ecessarily convex. We explore the relationship between thelarge N limit of
  the constant in the logarithmic Sobolev inequality(LSI) for the N-particl
 e system and the presence or absence of phasetransitions for the mean fiel
 d limit. The non-degeneracy of the LSIconstant will be shown to have far r
 eaching consequences\, especiallyin the context of uniform-in-time propaga
 tion of chaos and thebehaviour of equilibrium fluctuations. This will be d
 one by employingtechniques from the theory of gradient flows in the 2-Wass
 ersteindistance\, specifically the Riemannian calculus on the space ofprob
 ability measures.
LOCATION:Seminar Room 2\, Newton Institute
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