Poissonian bursts in e-mail correspondence

Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend this analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data are more correlated - bursty - than a Poisson process. Our analysis demonstrates that the correlations in the empirical data are indistinguishable from those of randomly reordered time series, illustrating that any correlations in the data are not due to the precise ordering of events. We further find that correlations in synthetic time series generated from a cascading Poisson process agree quite well with the correlations observed in the empirical data. Finally, we rescale the empirical time series to confirm that e-mail correspondence is no more correlated than expected from a suitably chosen Poisson process.