In a paper published in the SIAM Journal on Applied Mathematics, Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov, and Scott McCalla propose a mathematical model that analyzes criminal movement in terms of a Lévy flight.
Lévy flights are like standard random walks, except that a Lévy flight's step lengths are chosen from a power-law distribution. This allows the steps of a random walk to have large jumps. Modeling criminal movement using Lévy flights captures the fact that criminals supplement local movement with large leaps to other areas.
The researchers wonder where else consideration of Lévy flights might yield insight:
One of the surprising results in our model is that the criminals benefit very significantly by making a few big jumps while otherwise following a Brownian (or random) motion. It would be interesting to examine whether there are other situations, such as predator-prey models, where the optimal strategy is to follow nearly-Brownian motion with few jumps.
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