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Explore sharp quantitative results in the propagation of chaos phenomenon through this 43-minute mathematical conference talk. Learn how large systems of weakly interacting particles maintain approximate independence over time when initialized as such, with quantification through distances between low-dimensional marginal distributions and product measures. Discover recent advances in both classical mean field diffusions and non-exchangeable models, driven by a novel "local" relative entropy method that estimates low-dimensional marginals iteratively by adding coordinates one at a time. Understand how this approach yields surprising improvements over previous "global" arguments using subadditivity inequalities, and examine the unexpected connection with first-passage percolation in non-exchangeable settings. The presentation covers cutting-edge research in probability theory, specifically addressing mathematical frameworks for understanding particle systems and their statistical behavior in complex mathematical environments.
