The relationship between extremum statistics and universal fluctuations

Details The relationship between extremum statistics and universal fluctuations The relationship between extremum statistics and universal fluctuations

2000-07-17

arxiv.org/abs/cond-mat/0007275v3

Physics

Condensed Matter

Statistical Mechanics

6 pages, 1 figure. Paper submitted to PRL, 14th July 2000. Revised version re-submitted to PRL, 12th March, 2001. Paper reject

Scientific paper

The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the "global" PDF in terms of the "source" PDF of the individual events in the system. A single parameter distinguishes the global PDF and is related to the exponent of the source PDF. When normalized, the global PDF is shown to be insensitive to this parameter and importantly we obtain the previously demonstrated "universality" from an uncorrelated Gaussian source PDF. The second and third moments of the global PDF are more sensitive, providing a powerful tool to probe the degree of complexity of physical systems.

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