A fundamental question in the statistical physics of  complex systems is how spatial and temporal randomness may generate patterns and dynamics.

The dynamics of complex systems can be systematically analysed using diffusion equations and random-matrix theory.  This approach may yield, as experience shows, surprisingly universal, and in several cases analytically exact results. More importantly, the results show that at first sight unrelated phenomena observed in complex systems in a wide range of different disciplines (Biology, Condensed Matter Physics, and Fluid Dynamics) can be understood in terms of simple and thus general mechanisms.