Project B09
Mean field theories and scaling limits of nonlinear stochastic evolution systems

Project description

This project aims to develop mean field techniques for analyzing neural activity in large-scale biological neural networks, focusing on functional laws of large numbers for sparse, heterogeneous networks. It will explore homogenization limits with oscillating coefficients and their interaction with stochastic perturbations. The project will also investigate the emergence and stability of coherent structures, like travelling waves, in stochastic processes and extend functional central limit theorems to capture non-Gaussian fluctuations and multistability features. Later stages will refine the analysis for biologically realistic connectivity patterns and extend to quasilinear and non-smooth PDE systems in fluid dynamics. 

Principal Investigators

Marita Thomas (FU Berlin)

Wilhelm Stannat (TU Berlin)

Project members 

Owen Hearder (FU Berlin)

Publications

Preprints