A Poissonian explanation for heavy tails in e-mail communication

2008/11/18 by R. Dean Malmgren, Daniel B. Stouffer, Adilson E. Motter +2 · 8 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Astrophysics #Complex Network Analysis Techniques #Computer science #Diffusion and Search Dynamics #Econometrics #Event (particle physics) #Exponential distribution #Exponential function #Exponential growth #Heavy-tailed distribution #Homogeneous #Mathematics #Opinion Dynamics and Social Influence #Physics #Poisson distribution #Poisson process #Power law #Probability distribution #Proxy (statistics) #Scaling #Statistical physics #Statistics #cs.CY #physics.data-an #physics.soc-ph

paper · pdf · doi:10.1073/pnas.0800332105

published as PNAS 105(47): 18153-18158 (2008) · 9 pages, 5 figures

openalex publication_date 2008/11/18 · arxiv created 2009/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time tau between consecutively sent e-mails decays asymptotically as tau(-alpha), with alpha approximately 1. The slower-than-exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading nonhomogeneous Poisson process that explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems.

Citations

• Log-normal statistics in e-mail communication patterns
• Statistical physics of social dynamics
• Response time of internauts
• Spectra of some self-exciting and mutually exciting point processes
• Effective dynamics in Hamiltonian systems with mixed phase space
• The Structure and Function of Complex Networks

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