Levy strategies in intermittent search processes are advantageous

Intermittent search processes switch between local Brownian search events and ballistic relocation phases. We demonstrate analytically and numerically in one dimension that when relocation times are Levy distributed, resulting in a Levy walk dynamics, the search process significantly outperforms the previously investigated case of exponentially distributed relocation times: The resulting Levy walks reduce oversampling and thus further optimize the intermittent search strategy in the critical situation of rare targets. We also show that a searching agent that uses the Levy strategy is much less sensitive to the target density, which would require considerably less adaptation by the searcher.