Scaling laws in the dynamics of crime growth rate

TL;DR

This paper investigates the statistical properties of crime growth rates in Brazilian cities, revealing scale-invariant behavior and power-law decay relations, which contribute to understanding urban crime dynamics.

Contribution

It introduces a quantitative analysis of crime growth rates showing scale invariance and power-law relations, advancing the understanding of urban crime dynamics.

Findings

Logarithmic homicide growth rates follow a scale-invariant distribution.

Standard deviations of growth rates decay as a power law with city size.

Results suggest similarities between crime dynamics and complex organizational systems.

Abstract

The increasing number of crimes in areas with large concentrations of people have made cities one of the main sources of violence. Understanding characteristics of how crime rate expands and its relations with the cities size goes beyond an academic question, being a central issue for contemporary society. Here, we characterize and analyze quantitative aspects of murders in the period from 1980 to 2009 in Brazilian cities. We find that the distribution of the annual, biannual and triannual logarithmic homicide growth rates exhibit the same functional form for distinct scales, that is, a scale invariant behavior. We also identify asymptotic power-law decay relations between the standard deviations of these three growth rates and the initial size. Further, we discuss similarities with complex organizations.