Rudi Schäfer

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The understanding of complex systems has become a central issue because such systems exist in a wide range of scientific disciplines. We here focus on financial markets as an example of a complex system. In particular we analyze financial data from the S&P 500 stocks in the 19-year period 1992-2010. We propose a definition of state for a financial market(More)
We demonstrate that the lowest possible price change (tick-size) has a large impact on the structure of financial return distributions. It induces a microstructure as well as it can alter the tail behavior. On small return intervals, the tick-size can distort the calculation of correlations. This especially occurs on small return intervals and thus(More)
The scattering matrix was measured for microwave cavities with two antennas. It was analyzed in the regime of overlapping resonances. The theoretical description in terms of a statistical scattering matrix and the rescaled Breit-Wigner approximation has been applied to this regime. The experimental results for the auto-correlation function show that the(More)
Using supersymmetry techniques analytical expressions for the average of the fidelity amplitude f ǫ (τ) = ψ(0)| exp(2πıH ǫ τ) exp(−2πıH 0 τ)|ψ(0) are obtained, where the H 0 and H ǫ are taken from the Gaussian unitary ensemble (GUE) or the Gaussian orthogonal ensemble (GOE), and ǫ is a parameter, characterizing the strength of a perturbation. As long as the(More)
We here give an improved formalism for calculating the evolution of density fluctuations and temperature perturbations in flat universes. Our equations are general enough to treat the perturbations in collisionless relics like massive neutrinos. We find this formulation to be simpler to use than gauge dependent and other gauge–invariant formalisms. We show(More)
There are non–vanishing price responses across different stocks in correlated financial markets. We further study this issue by performing different averages, which identify active and passive cross– responses. The two average cross–responses show different characteristic dependences on the time lag. The passive cross–response exhibits a shorter response(More)
Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used.(More)
We present an extensive comparison of models of structure formation with observations , based on linear and quasi-linear theory. We assume a critical matter density, and study both cold dark matter models and cold plus hot dark matter models. We explore a wide range of parameters, by varying the fraction of hot dark matter Ω ν , the Hubble parameter h and(More)