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Abstract
Containing the spread of crime in urban societies remains a major challenge. Empirical
evidence suggests that, if left unchecked, crimes may be recurrent and proliferate.
On the other hand, eradicating a culture of crime may be difficult, especially under
extreme social circumstances that impair the creation of a shared sense of social
responsibility. Although our understanding of the mechanisms that drive the emergence
and diffusion of crime is still incomplete, recent research highlights applied mathematics
and methods of statistical physics as valuable theoretical resources that may help
us better understand criminal activity. We review different approaches aimed at modeling
and improving our understanding of crime, focusing on the nucleation of crime hotspots
using partial differential equations, self-exciting point process and agent-based
modeling, adversarial evolutionary games, and the network science behind the formation
of gangs and large-scale organized crime. We emphasize that statistical physics of
crime can relevantly inform the design of successful crime prevention strategies,
as well as improve the accuracy of expectations about how different policing interventions
should impact malicious human activity that deviates from social norms. We also outline
possible directions for future research, related to the effects of social and coevolving
networks and to the hierarchical growth of criminal structures due to self-organization.