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Abstract: Recent work has shown that the distribution of inter-event times for e-mailcommunication exhibits a heavy tail which is statistically consistent with acascading Poisson process. In this work we extend the analysis to higher-orderstatistics, using the Fano and Allan factors to quantify the extent to whichthe empirical data depart from the known correlations of Poissonian statistics.The analysis shows that the higher-order statistics from the empirical data isindistinguishable from that of randomly reordered time series, thusdemonstrating that e-mail correspondence is no more bursty or correlated than aPoisson process. Furthermore synthetic data sets generated by a cascadingPoisson process replicate the burstiness and correlations observed in theempirical data. Finally, a simple rescaling analysis using the best-estimaterate of activity, confirms that the empirically observed correlations arisefrom a non-homogeneus Poisson process.

Author: C. Anteneodo, R. Dean Malmgren, D. R. Chialvo

Source: https://arxiv.org/


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