Stochastic modeling of a serial killer

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M.V. Simkin and V.P. Roychowdhury: We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of  "Devil’s staircase" type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4.

We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We confirm analytical results by numerical simulation.

M.V. Simkin and V.P. Roychowdhury
Department of Electrical Engineering, University of California, Los Angeles, CA 90095-1594

Arxiv (1201.2458)