Stochastic modeling of a serial killer
Abstract
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 intermurder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 DOI:
 10.48550/arXiv.1201.2458
 arXiv:
 arXiv:1201.2458
 Bibcode:
 2012arXiv1201.2458S
 Keywords:

 Physics  Physics and Society;
 Quantitative Biology  Neurons and Cognition
 EPrint:
 Journal of Theoretical Biology (2014) 355: 111116