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From particle systems to nonlinear SPDEs
This mini-course gives an introduction to nonlinear SPDE models arising from particle systems, with a focus on the Dean–Kawasaki equation and related fluctuating hydrodynamic descriptions. Starting from empirical measures of stochastic particle dynamics, we will discuss formal derivations, modelling choices, and some of the key mathematical challenges, including well-posedness. The course will also introduce numerical approaches for these equations and highlight connections to collective behaviour, interacting particle systems, and applications.
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