Ana Durdevac, Freie Universität Berlin, will be presenting Nonlinear SPDE models of particle systems

Abstract. Interacting particle systems provide flexible and powerful models that are useful in many application areas such as sociology (agents), molecular dynamics (proteins) etc. However, particle systems with large numbers of particles are very complex and difficult to handle, both analytically and computationally. One of the common strategies is to derive effective equations that describe the time evolution of the empirical particle density.

We will study continuum models for the mesoscopic behavior of particles systems. In particular,  we are interested in finite size effects. More precisely, we will introduce nonlinear and non-Gaussian models that provide a more faithful representation of the evolution of the empirical density of a given particle system than the usual linear. A prototypical
example that we will consider is the formal identification of a finite system of diffusions with the singular Dean-Kawasaki SPDE. This is the joint work with H. Kremp and N. Perkowsk. Furthermore, we will discuss the application of these type of equations in the feedback-loop opinion dynamics, which is a joint work with Jonas Köppl and N. Dj. Conrad.