Los Angeles police are getting tip-offs from unlikely informants: mathematicians.

Using crime data from southern California, Jeffrey Brantingham of the University of California, Los Angeles, and his colleagues set out to calculate how the movements of criminals and victims create opportunities for crime, and how police can reduce it. They came up with a pair of equations that could explain how local crime hotspots form – which turned out to be similar to those that describe molecular reactions and diffusion.

The equations suggested that there are two kinds of hotspot. The first, called "supercritical", arises when small spikes in crime pass a certain threshold and create a local crime wave. The second, "subcritical", happens when a particular factor – the presence of a drug den, for instance – causes a large spike in crime. The equations also indicated that rigorous policing could completely eliminate the subcritical hotspots, but would simply displace the supercritical variety.

The approach "presents a novel hypothesis of how hotspots form", says John Eck, a criminologist at the University of Cincinnati, Ohio. Brantingham hopes eventually to be able to predict where subcritical hotspots are forming, so police can step in to nip problems in the bud. His team is already collaborating with Los Angeles police.