Regensburg 2013 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Statistical Physics (general)

DY 22.8: Vortrag

Mittwoch, 13. März 2013, 17:15–17:30, H48

From the number of detritus lines to hysteresis memory – On the statistics of dominant extreme values — •Sven Schubert and Günter Radons — Chemnitz University of Technology, 09107 Chemnitz, Germany

We are interested in the statistics of the number of dominant extreme values and its evolution in time. What are dominant maxima? They are to a time series what the pattern of seaweed and detritus residues on the beach is to the amplitudes of the arriving water waves.
In the first part of the talk, results are presented on the statistics of the number of dominant maxima of a sequence of i.i.d. continuous random variables. One finds that the number of dominant maxima is a nonstationary variable. It shows ageing and its expectation value is diverging logarithmically as the time approaches infinity.
The sequence of dominant maxima memorizes certain local maxima from a time series. This decreasing sequence of maxima is a simplified version of the memory of a Preisach model of hysteresis where an alternating series of dominant minima and maxima is stored. The second part of the talk elucidates this connection and discusses the implications of the results presented to the memory length of the Preisach model of hysteresis.