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Self-organised critical hot spots of criminal activity

Published online by Cambridge University Press:  07 July 2010

H. BERESTYCKI  and
J.-P. NADAL
H. BERESTYCKI
Affiliation:
Centre d'Analyse et de Mathématique Sociales (CAMS, UMR 8557 CNRS – EHESS), Ecole des Hautes Etudes en Sciences Sociales, 54 Bd. Raspail, 75270 Paris Cedex 06, France email: hb@ehess.fr
J.-P. NADAL
Affiliation:
Centre d'Analyse et de Mathématique Sociales (CAMS, UMR 8557 CNRS – EHESS), Ecole des Hautes Etudes en Sciences Sociales, 54 Bd. Raspail, 75270 Paris Cedex 06, France email: hb@ehess.fr Laboratoire de Physique Statistique (LPS, UMR 8550 CNRS – ENS – UPMC Univ. Paris 6 – Paris Diderot Paris 7), Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France email: nadal@lps.ens.fr
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Abstract

In this paper1 we introduce a family of models to describe the spatio-temporal dynamics of criminal activity. It is argued here that with a minimal set of mechanisms corresponding to elements that are basic in the study of crime, one can observe the formation of hot spots. By analysing the simplest versions of our model, we exhibit a self-organised critical state of illegal activities that we propose to call a warm spot or a tepid milieu2 depending on the context. It is characterised by a positive level of illegal or uncivil activity that maintains itself without exploding, in contrast with genuine hot spots where localised high level or peaks are being formed. Within our framework, we further investigate optimal policy issues under the constraint of limited resources in law enforcement and deterrence. We also introduce extensions of our model that take into account repeated victimisation effects, local and long range interactions, and briefly discuss some of the resulting effects such as hysteresis phenomena.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 4-5: Criminality , October 2010 , pp. 371 - 399
Copyright
Copyright © Cambridge University Press 2010

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