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Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions

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FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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