We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of...

In this paper (Part I) we extend the linear response analysis to calculate the complex dynamic susceptibility and the complex dynamic mobility/conductivity for a system in a transient state relaxing to equilibrium. This analysis has a meaning in the intermediate time and frequency region; for...

The authors investigate the random walk of a particle on a one-dimensional chain which has been constructed by a random-walk procedure. Exact expressions are given for the mean-square displacement and the fourth moment after n steps. The probability density after n steps is derived in the...