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Matias Gonzalo Delgadino (University of Texas at Austin)
Tuesday 22 February 2022, 14:50-15:35
Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions
- đ¤ Speaker: Matias Gonzalo Delgadino (University of Texas at Austin)
- đ Date & Time: Tuesday 22 February 2022, 14:50 - 15:35
- đ Venue: Seminar Room 2, Newton Institute
Abstract
In this talk, we will study the mean field limit of weaklyinteracting diffusions for confining and interaction potentials thatare not necessarily convex. We explore the relationship between thelarge N limit of the constant in the logarithmic Sobolev inequality(LSI) for the N-particle system and the presence or absence of phasetransitions for the mean field limit. The non-degeneracy of the LSIconstant will be shown to have far reaching consequences, especiallyin the context of uniform-in-time propagation of chaos and thebehaviour of equilibrium fluctuations. This will be done by employingtechniques from the theory of gradient flows in the 2-Wassersteindistance, specifically the Riemannian calculus on the space ofprobability measures.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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