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Factorial Moments in Complex Systems

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  • Laurent Schoeffel

    (CEA - Saclay)

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    Abstract

    Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. They include all correlations within the system of particles and represent integral characteristics of any correlation between these particles. In this letter, we show a direct comparison between high energy physics and quantitative finance results. Both for physics and finance, we illustrate that correlations between particles lead to a broadening of the multiplicity distribution and to dynamical fluctuations when the resolution becomes small enough. From the generating function of factorial moments, we make a prediction on the gap probability for sequences of returns of positive or negative signs. The gap is defined as the number of consecutive positive returns after a negative return, thus this is a gap in negative return. Inversely for a gap in positive return. Then, the gap probability is shown to be exponentially suppressed within the gap size. We confirm this prediction with data.

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    File URL: http://arxiv.org/pdf/1108.5946
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    Paper provided by arXiv.org in its series Papers with number 1108.5946.

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    Date of creation: Aug 2011
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    Handle: RePEc:arx:papers:1108.5946

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