| Abstract: |
| The Dean-Kawasaki equation was formally derived in the physics literature as a coarse-grained SPDE describing interacting particle systems on mesoscopic scales. However, as later discovered in the mathematics literature, it is really an exact rewriting of the particle system and does not allow for a coarse-graining interpretation. To go to mesoscopic scales, a posteriori truncations of the Dean-Kawasaki have been studied in recent years, and they have been shown to capture large deviations of the particle system, and the approximation error has been controlled quantitatively. In my talk, I will discuss the role of the maximum principle in such approximations: To obtain a superpolynomial approximation rate it seems necessary to consider approximations that violate the maximum principle. Those, however, are shown to achieve only a poor approximation if there is a ``vacuum ``i.e. spatial regions with no or very few particles. Joint work with Ana Djurdjevac. |
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