Speaker
Alexandra Holzinger, TU Wien
Abstract
In the study of mean-field limits, it is well known that the viscous porous media equation can be derived from a system of \(N\) moderately interacting particles in the limit \(N\rightarrow\infty\) (see e.g. Oelschläger ’85 and ’87). However, there are only very few results available concerning the rate of convergence in the mean-field limit for moderately interacting particles – especially when we are interested in algebraic rates of convergence which are important in order to show a central limit theorem for the particles in the moderate setting.
In this talk I will give an introduction to moderately interacting particles and explain how we can combine the convergence result in \(L^2\)-norm by Oelschläger ’87 with relative entropy methods for mean-field limits developed by Jabin and Wang in order to show a strong quantitative propagation of chaos result for the viscous porous medium equation in \(L^1\)-norm and algebraic rate \(N^{-\gamma}\) for some \(\gamma>0\). Additionally, I will explain the connection between the \(L^2\)-norm convergence result of Oelschläger and fluctuations around the mean-field limit as well as difficulties that arise for proving Oelschläger’s \(L^2\)-norm result for a more general class for moderate models.
This is joint work with Li Chen (University of Mannheim) and Xiaokai Huo (Iowa State University).