| Abstract | The interacting particle systems can not only be used as particle methods for solving PDEs but also can be adopted for statistical sampling. I will talk about the effects of interaction on the fluctuation of empirical measures. The systems with positive definite interaction potentials tend to exhibit smaller fluctuation while systems with negative definite potentials tend to exhibit larger fluctuation, compared to the fluctuation in standard Monte Carlo sampling. This phenomenon may give some understanding to physical systems, and may help to understand the properties of some particle based variational inference sampling methods. |
